UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                   FORM N-CSR

        CERTIFIED SHAREHOLDER REPORT OF REGISTERED MANAGEMENT INVESTMENT
                                   COMPANIES

                  Investment Company Act file number 811-22528
                                                    -----------

                     First Trust Energy Infrastructure Fund
         --------------------------------------------------------------
               (Exact name of registrant as specified in charter)

                       120 East Liberty Drive, Suite 400
                               Wheaton, IL 60187
         --------------------------------------------------------------
              (Address of principal executive offices) (Zip code)

                             W. Scott Jardine, Esq.

                          First Trust Portfolios L.P.
                       120 East Liberty Drive, Suite 400
                               Wheaton, IL 60187
         --------------------------------------------------------------
                    (Name and address of agent for service)

        registrant's telephone number, including area code: 630-765-8000
                                                           --------------

                      Date of fiscal year end: November 30
                                              -------------

                  Date of reporting period: November 30, 2016
                                           -------------------


Form N-CSR is to be used by management investment companies to file reports with
the Commission not later than 10 days after the transmission to stockholders of
any report that is required to be transmitted to stockholders under Rule 30e-1
under the Investment Company Act of 1940 (17 CFR 270.30e-1). The Commission may
use the information provided on Form N-CSR in its regulatory, disclosure review,
inspection, and policymaking roles.

A registrant is required to disclose the information specified by Form N-CSR,
and the Commission will make this information public. A registrant is not
required to respond to the collection of information contained in Form N-CSR
unless the Form displays a currently valid Office of Management and Budget
("OMB") control number. Please direct comments concerning the accuracy of the
information collection burden estimate and any suggestions for reducing the
burden to Secretary, Securities and Exchange Commission, 100 F Street, NE,
Washington, DC 20549. The OMB has reviewed this collection of information under
the clearance requirements of 44 U.S.C. ss. 3507.





ITEM 1. REPORTS TO STOCKHOLDERS.

The Report to Shareholders is attached herewith.


                                                                     FIRST TRUST
                                                ENERGY INFRASTRUCTURE FUND (FIF)
--------------------------------------------------------------------------------
                                                                   ANNUAL REPORT
                                                              FOR THE YEAR ENDED
                                                               NOVEMBER 30, 2016


ENERGY INCOME PARTNERS, LLC                                          FIRST TRUST





--------------------------------------------------------------------------------
TABLE OF CONTENTS
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                                 ANNUAL REPORT
                               NOVEMBER 30, 2016

Shareholder Letter...........................................................  1
At a Glance..................................................................  2
Portfolio Commentary.........................................................  3
Portfolio of Investments.....................................................  5
Statement of Assets and Liabilities.......................................... 10
Statement of Operations...................................................... 11
Statements of Changes in Net Assets.......................................... 12
Statement of Cash Flows...................................................... 13
Financial Highlights......................................................... 14
Notes to Financial Statements................................................ 15
Report of Independent Registered Public Accounting Firm...................... 23
Additional Information....................................................... 24
Board of Trustees and Officers............................................... 30
Privacy Policy............................................................... 32

                  CAUTION REGARDING FORWARD-LOOKING STATEMENTS

This report contains certain forward-looking statements within the meaning of
the Securities Act of 1933, as amended, and the Securities Exchange Act of 1934,
as amended. Forward-looking statements include statements regarding the goals,
beliefs, plans or current expectations of First Trust Advisors L.P. ("First
Trust" or the "Advisor") and/or Energy Income Partners, LLC ("EIP" or the
"Sub-Advisor") and their respective representatives, taking into account the
information currently available to them. Forward-looking statements include all
statements that do not relate solely to current or historical fact. For example,
forward-looking statements include the use of words such as "anticipate,"
"estimate," "intend," "expect," "believe," "plan," "may," "should," "would" or
other words that convey uncertainty of future events or outcomes.

Forward-looking statements involve known and unknown risks, uncertainties and
other factors that may cause the actual results, performance or achievements of
First Trust Energy Infrastructure Fund (the "Fund") to be materially different
from any future results, performance or achievements expressed or implied by the
forward-looking statements. When evaluating the information included in this
report, you are cautioned not to place undue reliance on these forward-looking
statements, which reflect the judgment of the Advisor and/or Sub-Advisor and
their respective representatives only as of the date hereof. We undertake no
obligation to publicly revise or update these forward-looking statements to
reflect events and circumstances that arise after the date hereof.

                          MANAGED DISTRIBUTION POLICY

The Board of Trustees of the Fund has approved a managed distribution policy for
the Fund (the "Plan") in reliance on exemptive relief received from the
Securities and Exchange Commission that permits the Fund to make periodic
distributions of long-term capital gains as frequently as monthly each tax year.
Under the Plan, the Fund currently intends to continue to pay a recurring
monthly distribution in the amount of $0.11 per Common Share that reflects the
distributable cash flow of the Fund. A portion of this monthly distribution may
include realized capital gains. This may result in a reduction of the long-term
capital gain distribution necessary at year end by distributing realized capital
gains throughout the year. The annual distribution rate is independent of the
Fund's performance during any particular period. Accordingly, you should not
draw any conclusions about the Fund's investment performance from the amount of
any distribution or from the terms of the Plan. The Board of Trustees may amend
or terminate the Plan at any time without prior notice to shareholders.

                        PERFORMANCE AND RISK DISCLOSURE

There is no assurance that the Fund will achieve its investment objective. The
Fund is subject to market risk, which is the possibility that the market values
of securities owned by the Fund will decline and that the value of the Fund
shares may therefore be less than what you paid for them. Accordingly, you can
lose money by investing in the Fund. See "Risk Considerations" in the Additional
Information section of this report for a discussion of certain other risks of
investing in the Fund.

Performance data quoted represents past performance, which is no guarantee of
future results, and current performance may be lower or higher than the figures
shown. For the most recent month-end performance figures, please visit
http://www.ftportfolios.com or speak with your financial advisor. Investment
returns, net asset value and common share price will fluctuate and Fund shares,
when sold, may be worth more or less than their original cost.

The Advisor may also periodically provide additional information on Fund
performance on the Fund's webpage at http://www.ftportfolios.com.

                            HOW TO READ THIS REPORT

This report contains information that may help you evaluate your investment in
the Fund. It includes details about the Fund and presents data and analysis that
provide insight into the Fund's performance and investment approach.

By reading the portfolio commentary by the portfolio management team of the
Fund, you may obtain an understanding of how the market environment affected the
Fund's performance. The statistical information that follows may help you
understand the Fund's performance compared to that of relevant market
benchmarks.

It is important to keep in mind that the opinions expressed by personnel of EIP
are just that: informed opinions. They should not be considered to be promises
or advice. The opinions, like the statistics, cover the period through the date
on the cover of this report. The material risks of investing in the Fund are
spelled out in the prospectus, the statement of additional information, this
report and other Fund regulatory filings.





--------------------------------------------------------------------------------
SHAREHOLDER LETTER
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                    ANNUAL LETTER FROM THE CHAIRMAN AND CEO
                               NOVEMBER 30, 2016


Dear Shareholders:

Thank you for your investment in First Trust Energy Infrastructure Fund.

First Trust Advisors L.P. ("First Trust") is pleased to provide you with the
annual report which contains detailed information about your investment for the
12 months ended November 30, 2016, including a market overview and a performance
analysis for the period. We encourage you to read this report and discuss it
with your financial advisor.

Early in 2016, many investors were concerned that the volatility witnessed in
the stock market in 2015 would continue, and it did. During the first six months
of the year, one of the events that affected the global markets was the "Brexit"
vote (where citizens in the UK voted to leave the European Union). Just a few
days after the historic vote, the global equity markets rebounded to close June
30, 2016 at a combined market capitalization of $62 trillion. As of November 30,
2016, the S&P 500(R) Index was up 8.49% calendar year-to-date, according to
Bloomberg. From November 30, 2015 through November 30, 2016, the S&P 500(R)
Index was also in positive territory at 8.06%. The last few months had investors
keenly watching the presidential election in anticipation of the outcome of the
vote and its effect on the stock market and economy.

On November 8, Donald J. Trump was elected to become the 45th president in our
country's history. While no one has a crystal ball and the ability to predict
how his presidency will shape the United States (and the world), there is no
doubt that Trump's populist message resonated for many Americans. Trump's
message of improving lives for the "average" American, while reducing the size
and scope of the federal government, also likely won him millions of votes. Many
of Trump's supporters believe that with his background in business, he will make
policy changes that will help grow the economy and continue to spur stock
markets. As with all change and a new administration, only time will tell.

The current bull market (measuring from March 9, 2009 through November 30, 2016)
is the second longest in history. First Trust believes that having a long-term
investment horizon and investing in quality products can help you reach your
goals, regardless of ups and downs in the market. We strive to provide quality
investment products, which has been one of the hallmarks of our firm since its
inception more than 25 years ago.

Thank you for giving First Trust the opportunity to be a part of your investment
plan. We value our relationship with you and will continue to focus on helping
investors like you reach your financial goals.

Sincerely,

/s/ James A. Bowen

James A. Bowen
Chairman of the Board of Trustees
Chief Executive Officer of First Trust Advisors L.P.


                                                                          Page 1





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
"AT A GLANCE"
AS OF NOVEMBER 30, 2016 (UNAUDITED)

-------------------------------------------------------------------
FUND STATISTICS
-------------------------------------------------------------------
Symbol on New York Stock Exchange                               FIF
Common Share Price                                           $18.83
Common Share Net Asset Value ("NAV")                         $19.32
Premium (Discount) to NAV                                     (2.54)%
Net Assets Applicable to Common Shares                 $339,029,316
Current Monthly Distribution per Common Share (1)           $0.1100
Current Annualized Distribution per Common Share            $1.3200
Current Distribution Rate on Closing Common Share Price (2)    7.01%
Current Distribution Rate on NAV (2)                           6.83%
-------------------------------------------------------------------


-------------------------------------------------------------------
          COMMON SHARE PRICE & NAV (WEEKLY CLOSING PRICE)
-------------------------------------------------------------------
            Common Share Price          NAV
11/15       16.16                       18.19
            14.24                       16.05
            13.05                       15.22
            13.30                       15.35
            14.87                       16.67
12/15       14.59                       16.54
            13.42                       15.66
            12.06                       14.53
            12.84                       15.23
1/16        13.97                       16.12
            13.74                       16.09
            12.92                       14.89
            13.62                       15.85
2/16        14.26                       16.17
            15.33                       16.88
            15.45                       17.04
            15.76                       17.52
3/16        15.01                       17.16
            15.14                       17.08
            15.04                       17.18
            15.33                       17.48
            16.29                       18.24
4/16        16.75                       18.48
            16.12                       18.15
            16.30                       18.34
            16.88                       18.56
5/16        16.53                       18.64
            16.79                       19.04
            17.05                       19.18
            16.67                       19.09
6/16        16.95                       19.21
            17.49                       19.75
            17.54                       19.69
            17.68                       20.07
            18.03                       20.20
7/16        17.70                       20.05
            17.62                       19.73
            17.75                       20.06
            17.97                       20.06
8/16        17.79                       19.64
            17.69                       19.70
            17.51                       19.58
            17.44                       19.46
            18.33                       20.18
9/16        19.19                       20.09
            18.36                       19.42
            18.39                       19.60
            19.16                       19.81
10/16       18.66                       19.61
            17.03                       18.54
            17.16                       18.49
            17.91                       18.86
            18.54                       19.37
11/16       18.83                       19.32




----------------------------------------------------------------------------------------------------------------
PERFORMANCE
----------------------------------------------------------------------------------------------------------------
                                                                                               Average Annual
                                                                                                Total Return
                                                                                             -------------------
                                                                                          
                                                    1 Year Ended        5 Years Ended        Inception (9/27/11)
                                                      11/30/16            11/30/16               to 11/30/16

FUND PERFORMANCE (3)
NAV                                                    18.35%               9.05%                  11.12%
Market Value                                           29.84%              10.15%                   9.60%

INDEX PERFORMANCE
Philadelphia Stock Exchange Utility Index              14.35%               9.02%                   9.45%
Alerian MLP Total Return Index                          9.28%               2.51%                   3.87%
Blended Index (4)                                      12.69%               6.28%                   7.18%
----------------------------------------------------------------------------------------------------------------



-------------------------------------------------------------------
                                                        % OF TOTAL
INDUSTRY CLASSIFICATION                                 INVESTMENTS
-------------------------------------------------------------------
Pipelines                                                  49.3%
Electric Power                                             38.5
Natural Gas Utility                                         3.8
Propane                                                     3.5
Coal                                                        2.3
Gathering & Processing                                      1.8
Water Utility                                               0.2
Other                                                       0.6
----------------------------------------------------------------
                                        Total             100.0%
                                                         =======

-------------------------------------------------------------------
                                                        % OF TOTAL
TOP 10 HOLDINGS                                         INVESTMENTS
-------------------------------------------------------------------
Enbridge Energy Management, LLC                             9.8%
TransCanada Corp.                                           5.5
Enterprise Products Partners, L.P.                          4.1
Enbridge Income Fund Holdings, Inc. (CAD)                   3.3
Williams (The) Cos., Inc.                                   3.0
American Electric Power Co., Inc.                           3.0
NextEra Energy, Inc.                                        2.9
Eversource Energy, L.P.                                     2.8
NextEra Energy Partners, L.P.                               2.6
Public Service Enterprise Group, Inc.                       2.5
----------------------------------------------------------------
                                        Total              39.5%
                                                         =======


(1)   Most recent distribution paid or declared through 11/30/2016. Subject to
      change in the future.

(2)   Distribution rates are calculated by annualizing the most recent
      distribution paid or declared through the report date and then dividing by
      Common Share Price or NAV, as applicable, as of 11/30/2016. Subject to
      change in the future.

(3)   Total return is based on the combination of reinvested dividend, capital
      gain and return of capital distributions, if any, at prices obtained by
      the Dividend Reinvestment Plan and changes in NAV per share for NAV
      returns and changes in Common Share Price for market value returns. Total
      returns do not reflect sales load and are not annualized for periods of
      less than one year. Past performance is not indicative of future results.

(4)   The blended index consists of the following: Philadelphia Stock Exchange
      Utility Index (50%) and Alerian MLP Total Return Index (50%).


Page 2





--------------------------------------------------------------------------------
PORTFOLIO COMMENTARY
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                                 ANNUAL REPORT
                         NOVEMBER 30, 2016 (UNAUDITED)


                                  SUB-ADVISOR

ENERGY INCOME PARTNERS, LLC

Energy Income Partners, LLC ("EIP" or the "Sub-Advisor"), located in Westport,
Connecticut, serves as the investment subadvisor to the First Trust Energy
Infrastructure Fund (the "Fund"). EIP was founded in 2003 to provide
professional asset management services in the area of energy-related master
limited partnerships ("MLPs") and other high payout securities such as pipeline
companies, power utilities, yield corporations ("YieldCos")1, and energy
infrastructure real estate investment trusts ("REITs"). EIP mainly focuses on
investments in energy-related infrastructure assets such as pipelines, power
transmission and distribution, petroleum storage and terminals that receive
fee-based or regulated income from their corporate and individual customers. EIP
manages or supervises approximately $5.4 billion of assets as of November 30,
2016. Private funds advised by EIP include a partnership for U.S. high net worth
individuals and an open-end mutual fund. EIP also serves as an advisor to
separately managed accounts for individuals and institutions and provides its
model portfolio to unified managed accounts. Finally, EIP serves as a
sub-advisor to three closed-end management investment companies in addition to
the Fund, an actively managed exchange-traded fund ("ETF"), a sleeve of an
actively managed ETF and a sleeve of a series of a variable insurance trust. EIP
is a registered investment advisor with the Securities and Exchange Commission.

                           PORTFOLIO MANAGEMENT TEAM

JAMES J. MURCHIE - CO-PORTFOLIO MANAGER, FOUNDER, CHIEF EXECUTIVE OFFICER AND
  PRINCIPAL OF ENERGY INCOME PARTNERS, LLC
EVA PAO - CO-PORTFOLIO MANAGER, PRINCIPAL OF ENERGY INCOME PARTNERS, LLC
JOHN TYSSELAND - CO-PORTFOLIO MANAGER, PRINCIPAL OF ENERGY INCOME PARTNERS, LLC

                                   COMMENTARY

FIRST TRUST ENERGY INFRASTRUCTURE FUND

The investment objective of the Fund is to seek a high level of total return
with an emphasis on current distributions paid to shareholders. The Fund pursues
its objective by investing primarily in securities of companies engaged in the
energy infrastructure sector. These companies principally include
publicly-traded MLPs and limited liability companies taxed as partnerships, MLP
affiliates, YieldCos, pipeline companies, utilities and other
infrastructure-related companies that derive at least 50% of their revenues from
operating or providing services in support of infrastructure assets such as
pipelines, power transmission and petroleum and natural gas storage in the
petroleum, natural gas and power generation industries (collectively, "Energy
Infrastructure Companies"). Under normal market conditions, the Fund invests at
least 80% of its managed assets (total asset value of the Fund minus the sum of
the Fund's liabilities other than the principal amount of borrowing) in
securities of Energy Infrastructure Companies. There can be no assurance that
the Fund will achieve its investment objective. The Fund may not be appropriate
for all investors.

MARKET RECAP

As measured by the Alerian MLP Total Return Index ("AMZX") and the Philadelphia
Stock Exchange Utility Index ("UTY"), the total return for the year ended
November 30, 2016 was 9.28% and 14.35%, respectively. These figures are
according to data collected from several sources, including Alerian Capital
Management and Bloomberg. While in the short term, share appreciation of Energy
Infrastructure Companies can be volatile, the Sub-Advisor believes that over the
longer term, such share appreciation will approximate growth in monthly cash
distributions and dividends per share. Over the last 10 years, growth in MLP
distributions and utility dividends has averaged 2.2% and 3.4%, respectively.
Over the last 12 months, the cash distributions of MLPs represented by the AMZX
decreased by about 12.5% and utilities increased by about 3.9%.2

PERFORMANCE ANALYSIS

On a net asset value ("NAV") basis, the Fund provided a total return3 of 18.35%,
including the reinvestment of distributions for the year ended November 30,
2016. This compares, according to collected data, to a 12.69% return for a
blended index consisting of the UTY (50%) and the AMZX (50%) (the "Blended
Index"). Unlike the Fund, the Blended Index does not incur fees and expenses. On
a market value basis, the Fund had a total return, including the reinvestment of


1     YieldCos are publicly-traded entities that own, operate and acquire
      contracted renewable and conventional generation and thermal and other
      infrastructure assets, which are generally not MLP-qualifying assets. Like
      MLPs, YieldCos generally seek to position themselves as vehicles for
      investors seeking stable and growing dividend income from a diversified
      portfolio of lower-risk, hiqh-quality assets.

2     Source: Alerian Capital Management, Bloomberg, EIP calculations.

3     Total return is based on the combination of reinvested dividends, capital
      gains and return of capital distributions, if any, at prices obtained by
      the Dividend Reinvestment Plan and changes in NAV per Common Share for NAV
      returns and changes in Common Share price for market value returns. Total
      returns do not reflect sales load and are not annualized for periods of
      less than one year. Past performance is not indicative of future results.


                                                                          Page 3





--------------------------------------------------------------------------------
PORTFOLIO COMMENTARY (CONTINUED)
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                                 ANNUAL REPORT
                         NOVEMBER 30, 2016 (UNAUDITED)

distributions, of 29.84% for the same period. As of November 30, 2016, the
Fund's market price per share was $18.83, while the NAV per Common Share was
$19.32, a discount of 2.54%. As of November 30, 2015, the Fund's market price
per share was $16.16, while the NAV per Common Share was $18.19, a discount of
11.16%.

The Fund maintained its regular monthly Common Share distribution of $0.11 per
share for the year ended November 30, 2016.

For the year ended November 30, 2016, the Fund's NAV outperformed the 12.69%
return of the Blended Index by 566 basis points. We believe our adherence to a
strategy of owning non-cyclical energy infrastructure companies in North America
with high dividend payout ratios across a number of diverse asset classes has
helped the Fund outperform the Blended Index. We believe the MLP structure and a
high payout ratio is only suitable for a narrow set of long-lived assets that
have stable non-cyclical cash flows, such as regulated pipelines or other
infrastructure assets that are legal or natural monopolies.

An important factor that affected the return of the Fund was its use of
financial leverage through the use of a line of credit. The Fund has a committed
facility agreement with The Bank of Nova Scotia, with a maximum commitment
amount of $130,000,000. The Fund uses leverage because the Sub-Advisor believes
that, over time, leverage can enhance total return for common shareholders.
However, the use of leverage can also increase the volatility of the Fund's NAV
and therefore volatility of the Fund's Common Share price. For example, if the
prices of securities held by the Fund decline, the effect of changes in common
share NAV and common shareholder total return loss is magnified by the use of
leverage. Conversely, leverage may enhance Common Share returns during periods
when the prices of securities held by the Fund generally are rising. Unlike the
Fund, AMZX and UTY are not leveraged. Leverage had a positive impact on the
performance of the Fund over this reporting period.

MARKET AND FUND OUTLOOK

MLPs continue to play an integral role in the restructuring of more diversified
energy conglomerates. This restructuring includes the creation by these more
diversified conglomerates of subsidiaries with high dividend payout ratios that
own assets with stable cash flows such as pipelines, storage terminals and
electric power assets with long-term fixed-price contracts. The restructuring
can also include the divestiture by some of the parent companies of most or all
of their cyclical businesses, leaving the parent company looking very similar to
an old-fashioned pipeline utility with a large holding in a subsidiary MLP. We
believe these diversified energy conglomerates are restructuring so that their
regulated infrastructure assets that have predictable cash flows may be better
valued by the market. In our opinion, the result is a better financing tool to
raise capital for the new energy infrastructure projects. This phenomenon is
beginning to spread to the power utility industry, but instead of spinning out
MLPs, diversified power companies are spinning out regular "C" corporations with
higher dividend payout ratios (relative to earnings).

From January 1, 2016 through November 30, 2016, the MLP asset class experienced
one IPO that raised $0.3 billion compared to nine IPOs that raised $4.9 billion
during the same time period in 2015. Reduced activity may be attributed to weak
MLP equity markets as many indexes were down sharply during the trailing 24
months. From January 1, 2016 through November 30, 2016, total MLP equity
issuance was down 15% to $15.6 billion compared to $18.4 billion over the same
time period in 2015. Total MLP debt transactions were down 44% to $20.9 billion
from January 1, 2016 through November 30, 2016, which compares to $37.1 billion
over the same time period in 2015, according to Barclays MLP Weekly.

Capital expenditures for the 20 companies that comprise the UTY Index were $79.8
billion for the first three calendar quarters of 2016. The capital expenditure
estimate for 2016 is $113.5 billion. This compares to $86.3 billion in 2014 and
about $100.3 billion in 2015. (Source: Bloomberg) The expenditures are in
response to needs such as reliability, interconnection, modernization and
growing demand. These capital investments are supported, in part, by federal and
state regulation, which allows companies to recoup investments they have made in
the rates they charge their customers.

The Fund continues to seek to weight the portfolio toward Energy Infrastructure
Companies with mostly non-cyclical cash flows, investment-grade ratings,
conservative balance sheets, modest and/or flexible organic growth commitments
and available liquidity under revolving lines of credit. Since the Fund invests
in securities that tend to have high dividend payout ratios (relative to
earnings), in EIP's opinion, securities with unpredictable cyclical cash flows
make a poor fit within the portfolio. While there are some businesses within the
Fund's portfolio whose cash flows are cyclical, they are generally small and
analyzed in the context of each company's financial and operating leverage and
payout ratio.


Page 4





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS
NOVEMBER 30, 2016



   SHARES                                      DESCRIPTION                                       VALUE
------------  -----------------------------------------------------------------------------  --------------
COMMON STOCKS - 95.7%

                                                                                       
              ELECTRIC UTILITIES - 27.5%
     224,000  American Electric Power Co., Inc. (a)........................................  $   13,227,200
     147,600  Duke Energy Corp. (a)........................................................      10,888,452
      15,000  Edison International.........................................................       1,031,550
     190,600  Emera, Inc. (CAD) (a)........................................................       6,400,630
     244,400  Eversource Energy (a)........................................................      12,615,928
     307,100  Exelon Corp. (a).............................................................       9,983,821
     159,900  Fortis, Inc. (CAD) (a).......................................................       4,766,170
     256,200  Hydro One Ltd. (CAD) (a) (b).................................................       4,401,917
      62,200  IDACORP, Inc. (a)............................................................       4,736,530
     113,000  NextEra Energy, Inc. (a).....................................................      12,907,990
     138,700  Southern (The) Co. (a).......................................................       6,493,934
     147,900  Xcel Energy, Inc. (a)........................................................       5,769,579
                                                                                             --------------
                                                                                                 93,223,701
                                                                                             --------------

              GAS UTILITIES - 5.7%
      43,800  Atmos Energy Corp. (a).......................................................       3,115,056
      82,610  Chesapeake Utilities Corp. (a)...............................................       5,353,128
     131,000  New Jersey Resources Corp. (a)...............................................       4,512,950
     142,718  UGI Corp.....................................................................       6,393,767
                                                                                             --------------
                                                                                                 19,374,901
                                                                                             --------------

              MULTI-UTILITIES - 20.3%
      87,300  Alliant Energy Corp. (a).....................................................       3,135,816
     155,800  ATCO, Ltd., Class I (CAD) (a)................................................       4,964,073
     204,400  Canadian Utilities Ltd., Class A (CAD) (a)...................................       5,381,991
     158,300  CMS Energy Corp..............................................................       6,366,826
     144,500  National Grid PLC, ADR (a)...................................................       8,246,615
     173,400  NiSource, Inc. (a)...........................................................       3,804,396
     272,900  Public Service Enterprise Group, Inc. (a)....................................      11,273,499
     138,400  SCANA Corp. (a)..............................................................       9,761,352
      82,300  Sempra Energy (a)............................................................       8,213,540
     133,700  WEC Energy Group, Inc. (a)...................................................       7,488,537
                                                                                             --------------
                                                                                                 68,636,645
                                                                                             --------------

              OIL, GAS & CONSUMABLE FUELS - 41.9%
   1,751,179  Enbridge Energy Management, LLC (a) (c)......................................      43,744,452
     573,300  Enbridge Income Fund Holdings, Inc. (CAD) (a)................................      14,574,700
     130,000  Enbridge, Inc................................................................       5,465,200
     314,700  Inter Pipeline, Ltd. (CAD) (a)...............................................       6,398,018
     166,600  Keyera Corp. (CAD) (a).......................................................       4,788,525
     359,575  Kinder Morgan, Inc. (a)......................................................       7,982,565
     168,200  ONEOK, Inc...................................................................       9,239,226
     180,500  Plains GP Holdings L.P.......................................................       6,346,380
     106,100  Targa Resources Corp (a).....................................................       5,654,069
     545,570  TransCanada Corp. (a)........................................................      24,457,903
     436,500  Williams (The) Cos., Inc. (a)................................................      13,400,550
                                                                                             --------------
                                                                                                142,051,588
                                                                                             --------------

              WATER UTILITIES - 0.3%
      15,000  American Water Works Co., Inc. (a)...........................................       1,087,050
                                                                                             --------------
              TOTAL COMMON STOCKS..........................................................     324,373,885
              (Cost $308,225,447)                                                            --------------



                        See Notes to Financial Statements                 Page 5





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
NOVEMBER 30, 2016



  SHARES/
   UNITS                                       DESCRIPTION                                       VALUE
------------  -----------------------------------------------------------------------------  --------------
MASTER LIMITED PARTNERSHIPS - 34.8%

                                                                                       
              CHEMICALS - 0.1%
      22,000  Westlake Chemical Partners, L.P. (a).........................................  $      462,000
                                                                                             --------------

              GAS UTILITIES - 2.7%
     122,152  AmeriGas Partners, L.P. (a)..................................................       5,482,182
     126,900  Suburban Propane Partners, L.P. (a)..........................................       3,595,077
                                                                                             --------------
                                                                                                  9,077,259
                                                                                             --------------

              INDEPENDENT POWER AND RENEWABLE ELECTRICITY PRODUCERS - 3.4%
     445,455  NextEra Energy Partners, L.P. (a) (d)........................................      11,408,102
                                                                                             --------------

              OIL, GAS & CONSUMABLE FUELS - 28.6%
      79,700  Alliance Holdings GP, L.P. (a)...............................................       2,308,112
     339,930  Alliance Resource Partners, L.P. (a).........................................       8,056,341
      65,700  Buckeye Partners, L.P. (a)...................................................       4,227,138
     262,800  Columbia Pipeline Partners, L.P. (a).........................................       4,507,020
      26,500  Dominion Midstream Partners, L.P.............................................         678,400
      38,600  Enbridge Energy Partners, L.P. (a)...........................................         953,420
     707,700  Enterprise Products Partners, L.P. (a).......................................      18,350,661
     139,200  EQT Midstream Partners, L.P. (a).............................................      10,193,616
     214,676  Holly Energy Partners, L.P. (a)..............................................       6,925,448
     113,300  Magellan Midstream Partners, L.P. (a)........................................       7,846,025
     123,972  NGL Energy Partners, L.P. (a)................................................       2,299,681
     111,700  ONEOK Partners, L.P. (a).....................................................       4,669,060
      62,400  Phillips 66 Partners, L.P....................................................       2,816,112
      41,000  Shell Midstream Partners, L.P................................................       1,130,780
     250,300  Spectra Energy Partners, L.P. (a)............................................      10,635,247
      47,328  Tallgrass Energy Partners, L.P. (a)..........................................       2,216,843
     131,495  TC PipeLines, L.P. (a).......................................................       6,988,959
      56,002  TransMontaigne Partners, L.P. (a)............................................       2,379,525
                                                                                             --------------
                                                                                                 97,182,388
                                                                                             --------------
              TOTAL MASTER LIMITED PARTNERSHIPS............................................     118,129,749
              (Cost $102,541,817)                                                            --------------

REAL ESTATE INVESTMENT TRUSTS - 1.2%

              EQUITY REAL ESTATE INVESTMENT TRUSTS - 1.2%
     137,550  InfraREIT, Inc. (a)..........................................................       2,357,607
      49,101  CorEnergy Infrastructure Trust, Inc..........................................       1,607,076
                                                                                             --------------
              TOTAL REAL ESTATE INVESTMENT TRUSTS..........................................       3,964,683
              (Cost $4,519,858)                                                              --------------

              TOTAL INVESTMENTS - 131.7%...................................................     446,468,317
              (Cost $415,287,122) (e)                                                        --------------

 NUMBER OF
 CONTRACTS                                     DESCRIPTION                                       VALUE
------------  -----------------------------------------------------------------------------  --------------
CALL OPTIONS WRITTEN - (0.4%)

              AMERICAN ELECTRIC POWER CO., INC. CALL
       1,600  @ $62.50 due February 2017...................................................        (120,000)
                                                                                             --------------

              CMS ENERGY CORP. CALL
       1,100  @  45.00 due March 2017......................................................         (44,000)
                                                                                             --------------



Page 6                  See Notes to Financial Statements





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
NOVEMBER 30, 2016



 NUMBER OF
 CONTRACTS                                     DESCRIPTION                                       VALUE
------------  -----------------------------------------------------------------------------  --------------
CALL OPTIONS WRITTEN (CONTINUED)

                                                                                       
              DUKE ENERGY CORP. CALLS
         300  @ $77.50 due January 2017....................................................  $      (21,000)
         500  @  85.00 due January 2017....................................................          (2,500)
         300  @  87.50 due January 2017....................................................          (1,500)
                                                                                             --------------
                                                                                                    (25,000)
                                                                                             --------------

              ENBRIDGE, INC. CALLS
         400  @  45.00 due December 2016...................................................         (11,600)
         800  @  45.00 due January 2017....................................................         (60,800)
                                                                                             --------------
                                                                                                    (72,400)
                                                                                             --------------

              EVERSOURCE ENERGY CALLS
         200  @  60.00 due January 2017 (f)................................................          (2,000)
       1,200  @  65.00 due January 2017 (f)................................................         (36,000)
         400  @  60.00 due April 2017......................................................         (16,000)
                                                                                             --------------
                                                                                                    (54,000)
                                                                                             --------------

              EXELON CORP. CALLS
       1,500  @  34.00 due December 2016...................................................         (30,000)
         600  @  34.00 due January 2017....................................................         (33,000)
         100  @  35.00 due January 2017....................................................          (3,000)
         100  @  37.00 due January 2017....................................................            (500)
                                                                                             --------------
                                                                                                    (66,500)
                                                                                             --------------

              KINDER MORGAN, INC. CALLS
       1,800  @  23.00 due December 2016...................................................         (52,200)
       1,200  @  23.00 due March 2017......................................................        (138,000)
                                                                                             --------------
                                                                                                   (190,200)
                                                                                             --------------

              ONEOK, INC. CALL
       1,600  @  52.50 due December 2016...................................................        (512,000)
                                                                                             --------------

              SCANA CORP. CALL
       1,000  @  75.00 due February 2017...................................................         (82,000)
                                                                                             --------------

              SEMPRA ENERGY CALL
         600  @  105.00 due December 2016..................................................         (24,000)
                                                                                             --------------

              SOUTHERN (THE) CO. CALLS
         500  @   50.00 due January 2017...................................................         (14,500)
         500  @   55.00 due January 2017...................................................          (1,000)
                                                                                             --------------
                                                                                                    (15,500)
                                                                                             --------------

              TRANSCANADA CORP. CALLS
       3,500  @  50.00 due January 2017....................................................         (43,750)
         500  @  50.00 due May 2017........................................................         (32,500)
                                                                                             --------------
                                                                                                    (76,250)
                                                                                             --------------

              UGI CORP. CALL
       1,000  @  50.00 due April 2017......................................................         (50,000)
                                                                                             --------------

              WILLIAMS (THE) COS., INC. CALLS
       2,000  @  32.00 due December 2016...................................................         (76,000)
         500  @  32.00 due February 2017...................................................         (78,000)
                                                                                             --------------
                                                                                                   (154,000)
                                                                                             --------------
              TOTAL CALL OPTIONS WRITTEN...................................................      (1,485,850)
              (Premiums received $1,367,185)                                                 --------------



                        See Notes to Financial Statements                 Page 7





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
NOVEMBER 30, 2016



                                               DESCRIPTION                                       VALUE
              -----------------------------------------------------------------------------  --------------
                                                                                       
              OUTSTANDING LOAN - (35.8%)...................................................  $ (121,500,000)

              NET OTHER ASSETS AND LIABILITIES - 4.5%......................................      15,546,849
                                                                                             --------------
              NET ASSETS - 100.0%..........................................................  $  339,029,316
                                                                                             ==============


-----------------------------

(a)   All or a portion of this security serves as collateral on the outstanding
      loan.

(b)   This security is restricted in the U.S. and cannot be offered for public
      sale without first being registered under the Securities Act of 1933, as
      amended. This security is not restricted on the foreign exchange where it
      trades freely without any additional registration. As such, it does not
      require the additional disclosure required of restricted securities.

(c)   Non-income producing security that makes payment-in-kind ("PIK")
      distributions. For the fiscal year ended November 30, 2016, the Fund
      received 171,334 PIK shares of Enbridge Energy Management, LLC.

(d)   NextEra Energy Partners, L.P. is taxed as a "C" corporation for federal
      income tax purposes.

(e)   Aggregate cost for federal income tax purposes is $410,279,467. As of
      November 30, 2016, the aggregate gross unrealized appreciation for all
      securities in which there was an excess of value over tax cost was
      $50,059,756 and the aggregate gross unrealized depreciation for all
      securities in which there was an excess of tax cost over value was
      $13,870,906.

(f)   This security is fair valued by the First Trust Advisors L.P.'s Pricing
      Committee in accordance with procedures adopted by the Fund's Board of
      Trustees, and in accordance with the provisions of the Investment Company
      Act of 1940, as amended. At November 30, 2016, securities noted as such
      are valued at $(38,000) or (0.0)% of net assets.

ADR   American Depositary Receipt

CAD   Canadian Dollar - Security is denominated in Canadian Dollars and is
      translated into U.S. Dollars based upon the current exchange rate.

---------------------------------------


INTEREST RATE SWAP AGREEMENTS:
                                                              NOTIONAL
   COUNTERPARTY       FLOATING RATE (1)   EXPIRATION DATE      AMOUNT       FIXED RATE(1)       VALUE
----------------------------------------------------------------------------------------------------------
                                                                             
Bank of Nova Scotia   1 month LIBOR          10/08/20       $   36,475,000      2.121%      $     (929,373)
Bank of Nova Scotia   1 month LIBOR          09/03/24           36,475,000      2.367%          (1,221,510)
                                                            --------------                  --------------
                                                            $   72,950,000                  $   (2,150,883)
                                                            ==============                  ==============


(1)   The Fund pays the fixed rate and receives the floating rate. The floating
      rate on November 30, 2016 was 0.535% and 0.530%, respectively.


Page 8                  See Notes to Financial Statements





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
NOVEMBER 30, 2016

-----------------------------
VALUATION INPUTS

A summary of the inputs used to value the Fund's investments as of November 30,
2016 is as follows (see Note 3A - Portfolio Valuation in the Notes to Financial
Statements):



                                                    ASSETS TABLE
                                                                                         LEVEL 2          LEVEL 3
                                                        TOTAL           LEVEL 1        SIGNIFICANT      SIGNIFICANT
                                                       VALUE AT          QUOTED         OBSERVABLE      UNOBSERVABLE
                                                      11/30/2016         PRICES           INPUTS           INPUTS
                                                     ------------     ------------     ------------     ------------
                                                                                            
Common Stocks*.....................................  $324,373,885     $324,373,885     $         --     $         --
Master Limited Partnerships*.......................   118,129,749      118,129,749               --               --
Real Estate Investment Trusts*.....................     3,964,683        3,964,683               --               --
                                                     ------------     ------------     ------------     ------------
Total Investments..................................  $446,468,317     $446,468,317     $         --     $         --
                                                     ============     ============     ============     ============


                                               LIABILITIES TABLE
                                                                                         LEVEL 2          LEVEL 3
                                                        TOTAL           LEVEL 1        SIGNIFICANT      SIGNIFICANT
                                                       VALUE AT          QUOTED         OBSERVABLE      UNOBSERVABLE
                                                      11/30/2016         PRICES           INPUTS           INPUTS
                                                     ------------     ------------     ------------     ------------
Call Options Written..............................   $ (1,485,850)    $ (1,266,100)    $   (219,750)    $         --
Interest Rate Swaps**.............................     (2,150,883)              --       (2,150,883)              --
                                                     ------------     ------------     ------------     ------------
Total.............................................   $ (3,636,733)    $ (1,266,100)    $ (2,370,633)    $         --
                                                     ============     ============     ============     ============


*  See Portfolio of Investments for industry breakout.
** See Interest Rate Swap Agreements for contract detail.

All transfers in and out of the Levels during the period are assumed to be
transferred on the last day of the period at their current value. There were no
transfers between Levels at November 30, 2016.


                        See Notes to Financial Statements                 Page 9





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
STATEMENT OF ASSETS AND LIABILITIES
NOVEMBER 30, 2016



                                                                                               
ASSETS:
Investments, at value
     (Cost $415,287,122)........................................................................  $  446,468,317
Cash............................................................................................      18,575,559
Cash segregated as collateral for open swap contracts...........................................       5,664,059
Receivables:
     Investment securities sold.................................................................       5,778,247
     Dividends..................................................................................         966,995
     Interest...................................................................................             152
Prepaid expenses................................................................................           2,078
                                                                                                  --------------
     Total Assets...............................................................................     477,455,407
                                                                                                  --------------

LIABILITIES:
Outstanding loan................................................................................     121,500,000
Options written, at value (Premiums received $1,367,185)........................................       1,485,850
Swap contracts, at value ($569).................................................................       2,150,883
Payables:
     Investment securities purchased............................................................      12,604,251
     Investment advisory fees...................................................................         372,612
     Interest and fees on loan..................................................................         158,929
     Audit and tax fees.........................................................................          51,490
     Printing fees..............................................................................          45,425
     Custodian fees.............................................................................          20,388
     Administrative fees........................................................................          19,450
     Transfer agent fees........................................................................           5,405
     Legal fees.................................................................................           4,515
     Trustees' fees and expenses................................................................           2,938
     Financial reporting fees...................................................................             771
Other liabilities...............................................................................           3,184
                                                                                                  --------------
     Total Liabilities..........................................................................     138,426,091
                                                                                                  --------------
NET ASSETS......................................................................................  $  339,029,316
                                                                                                  ==============

NET ASSETS CONSIST OF:
Paid-in capital.................................................................................  $  312,305,171
Par value.......................................................................................         175,502
Accumulated net investment income (loss)........................................................       9,588,502
Accumulated net realized gain (loss) on investments, written options, swap
  contracts and

   foreign currency transactions................................................................     (11,951,635)
Net unrealized appreciation (depreciation) on investments, written options, swap
  contracts and

   foreign currency translation.................................................................      28,911,776
                                                                                                  --------------
NET ASSETS......................................................................................  $  339,029,316
                                                                                                  ==============
NET ASSET VALUE, per Common Share (par value $0.01 per Common Share)............................  $        19.32
                                                                                                  ==============
Number of Common Shares outstanding (unlimited number of Common Shares has been authorized).....      17,550,236
                                                                                                  ==============



Page 10                  See Notes to Financial Statements





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
STATEMENT OF OPERATIONS
FOR THE YEAR ENDED NOVEMBER 30, 2016



                                                                                               
INVESTMENT INCOME:
Dividends (net of foreign withholding tax of $499,637)..........................................  $    9,840,327
Interest........................................................................................           2,936
                                                                                                  --------------
     Total investment income....................................................................       9,843,263
                                                                                                  --------------

EXPENSES:
Investment advisory fees........................................................................       4,282,961
Interest and fees on loan.......................................................................       1,314,370
Administrative fees.............................................................................         211,000
Printing fees...................................................................................         187,291
Audit and tax fees..............................................................................          52,680
Custodian fees..................................................................................          51,021
Transfer agent fees.............................................................................          29,358
Trustees' fees and expenses.....................................................................          18,010
Legal fees......................................................................................          11,529
Financial reporting fees........................................................................           9,250
Other...........................................................................................          55,020
                                                                                                  --------------
     Total expenses.............................................................................       6,222,490
                                                                                                  --------------
NET INVESTMENT INCOME (LOSS)....................................................................       3,620,773
                                                                                                  --------------

NET REALIZED AND UNREALIZED GAIN (LOSS):
Net realized gain (loss) on:
     Investments................................................................................     (12,079,299)
     Written options............................................................................        (104,215)
     Swap contracts.............................................................................      (1,339,446)
     Foreign currency transactions..............................................................         (94,441)
                                                                                                  --------------
Net realized gain (loss)........................................................................     (13,617,401)
                                                                                                  --------------
Net increase from payment by the sub-advisor....................................................           1,600
                                                                                                  --------------
Net change in unrealized appreciation (depreciation) on:
     Investments................................................................................      58,851,468
     Written options............................................................................        (765,736)
     Swap contracts.............................................................................         786,229
     Foreign currency translation...............................................................           4,063
                                                                                                  --------------
Net change in unrealized appreciation (depreciation)............................................      58,876,024
                                                                                                  --------------
NET REALIZED AND UNREALIZED GAIN (LOSS).........................................................      45,260,223
                                                                                                  --------------
NET INCREASE (DECREASE)  IN NET ASSETS RESULTING FROM OPERATIONS................................  $   48,880,996
                                                                                                  ==============



                        See Notes to Financial Statements                Page 11





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
STATEMENTS OF CHANGES IN NET ASSETS



                                                                                           FOR THE           FOR THE
                                                                                             YEAR              YEAR
                                                                                            ENDED             ENDED
                                                                                          11/30/2016        11/30/2015
                                                                                        --------------    --------------
                                                                                                    
OPERATIONS:
Net investment income (loss).........................................................   $    3,620,773      $  5,952,005
Net realized gain (loss).............................................................      (13,617,401)       23,813,670
Net increase from payment by the sub-advisor.........................................            1,600                --
Net change in unrealized appreciation (depreciation).................................       58,876,024      (143,166,381)
                                                                                        --------------    --------------
Net increase (decrease) in net assets resulting from operations......................       48,880,996      (113,400,706)
                                                                                        --------------    --------------

DISTRIBUTIONS TO SHAREHOLDERS FROM:
Net investment income................................................................       (3,981,810)       (6,311,176)
Net realized gain....................................................................       (5,326,861)      (16,855,136)
Return of capital....................................................................      (19,824,721)               --
                                                                                        --------------    --------------
Total distributions to shareholders..................................................      (29,133,392)      (23,166,312)
                                                                                        --------------    --------------
Total increase (decrease) in net assets..............................................       19,747,604      (136,567,018)

NET ASSETS:
Beginning of period..................................................................      319,281,712       455,848,730
                                                                                        --------------    --------------
End of period........................................................................   $  339,029,316    $  319,281,712
                                                                                        ==============    ==============
Accumulated net investment income (loss) at end of period............................   $    9,588,502    $   12,580,015
                                                                                        ==============    ==============

COMMON SHARES:
Common Shares at end of period*......................................................       17,550,236        17,550,236
                                                                                        ==============    ==============



-----------------------------

*  On September 15, 2016, the Fund commenced a share repurchase program. The
   program will continue until the earlier of (i) the repurchase of 877,512
   common shares or (ii) March 15, 2017. Since September 15, 2016, the Fund
   has not repurchased any common shares.


Page 12                 See Notes to Financial Statements





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
STATEMENT OF CASH FLOWS
FOR THE YEAR ENDED NOVEMBER 30, 2016



                                                                                              
CASH FLOWS FROM OPERATING ACTIVITIES:
Net increase (decrease) in net assets resulting from operations ..........  $   48,880,996
Adjustments to reconcile net increase (decrease) in net assets
  resulting from operations to net cash provided by operating activities:
   Purchases of investments...............................................    (279,192,328)
   Sales of investments...................................................     296,340,279
   Proceeds from written options..........................................       7,330,129
   Amount paid to close written options...................................      (5,060,591)
   Return of capital distributions received from investment in MLPs
     and REITs............................................................       8,246,351
   Net realized gain/loss on investments and written options..............      12,183,514
   Net increase from payment by sub-advisor...............................          (1,600)
   Net change in unrealized appreciation/depreciation on investments and
     written options......................................................     (58,085,732)
   Net change in unrealized appreciation/depreciation on swap contracts...        (786,229)
   Increase in cash segregated as collateral for open swap contracts......        (310,554)

CHANGES IN ASSETS AND LIABILITIES:
   Increase in interest receivable........................................             (97)
   Decrease in dividends receivable.......................................          79,441
   Decrease in prepaid expenses...........................................           5,261
   Increase in interest and fees on loan payable..........................          57,295
   Increase in investment advisory fees payable...........................           4,824
   Increase in audit and tax fees payable.................................           1,190
   Increase in legal fees payable.........................................           1,063
   Increase in printing fees payable......................................           9,909
   Decrease in administrative fees payable................................            (193)
   Increase in custodian fees payable.....................................          11,472
   Increase in transfer agent fees payable................................           2,516
   Decrease in Trustees' fees and expenses payable........................            (404)
   Increase in other liabilities payable..................................           2,800
                                                                            --------------
CASH PROVIDED BY OPERATING ACTIVITIES.....................................                          $   29,719,312
                                                                                                    --------------

CASH FLOWS FROM FINANCING ACTIVITIES:
   Distributions to Common Shareholders from net investment income........      (3,981,810)
   Distributions to Common Shareholders from net realized gain............      (5,326,861)
   Distributions to Common Shareholders from return of capital............     (19,824,721)
   Proceeds from borrowing................................................      27,000,000
   Repayment of borrowing.................................................     (16,000,000)
                                                                            --------------
CASH USED IN FINANCING ACTIVITIES.........................................                             (18,133,392)
                                                                                                    --------------
Increase in cash and foreign currency (a).................................                              11,585,920
Cash and foreign currency at beginning of period..........................                               6,989,639
                                                                                                    --------------
CASH AND FOREIGN CURRENCY AT END OF PERIOD................................                          $   18,575,559
                                                                                                    ==============

SUPPLEMENTAL DISCLOSURE OF CASH FLOW INFORMATION:
Cash paid during the period for interest and fees.........................                          $    1,257,075
                                                                                                    ==============



-----------------------------

(a)   Includes net change in unrealized appreciation (depreciation) on foreign
      currency of $4,063.


                        See Notes to Financial Statements                Page 13





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
FINANCIAL HIGHLIGHTS
FOR A COMMON SHARE OUTSTANDING THROUGHOUT EACH PERIOD



                                                                             YEAR ENDED NOVEMBER 30,
                                                      ----------------------------------------------------------------------
                                                         2016           2015           2014           2013           2012
                                                      ----------     ----------     ----------     ----------     ----------
                                                                                                   
Net asset value, beginning of period................. $    18.19     $    25.97     $    22.30     $    22.74     $    21.38
                                                      ----------     ----------     ----------     ----------     ----------
INCOME FROM INVESTMENT OPERATIONS:
Net investment income (loss).........................       0.21           0.34           0.22           0.22           0.27
Net realized and unrealized gain (loss)..............       2.58 (a)      (6.80)          6.20           3.47 (a)       2.38 (a)
                                                      ----------     ----------     ----------     ----------     ----------
Total from investment operations.....................       2.79          (6.46)          6.42           3.69           2.65
                                                      ----------     ----------     ----------     ----------     ----------
Common Shares offering costs charged to paid-in
   capital...........................................         --             --             --             --           0.01
                                                      ----------     ----------     ----------     ----------     ----------
DISTRIBUTIONS PAID TO SHAREHOLDERS FROM:
Net investment income................................      (0.23)         (0.36)         (0.45)         (0.83)         (1.01)
Net realized gain....................................      (0.30)         (0.96)         (2.21)         (3.25)         (0.29)
Return of capital....................................      (1.13)            --          (0.09)         (0.05)            --
                                                      ----------     ----------     ----------     ----------     ----------
Total distributions to Common Shareholders...........      (1.66)         (1.32)         (2.75)         (4.13)         (1.30)
                                                      ----------     ----------     ----------     ----------     ----------
Net asset value, end of period....................... $    19.32     $    18.19     $    25.97     $    22.30     $    22.74
                                                      ==========     ==========     ==========     ==========     ==========
Market value, end of period.......................... $    18.83     $    16.16     $    23.00     $    21.71     $    21.34
                                                      ==========     ==========     ==========     ==========     ==========
TOTAL RETURN BASED ON NET ASSET VALUE (b)............      18.35% (a)    (25.29)%        31.02%         17.76% (a)     13.08% (a)
                                                      ==========     ==========     ==========     ==========     ==========
TOTAL RETURN BASED ON MARKET VALUE (b)...............      29.84%        (25.05)%        19.18%         22.11%         14.47%
                                                      ==========     ==========     ==========     ==========     ==========
--------------------

RATIOS TO AVERAGE NET ASSETS/SUPPLEMENTAL DATA:
Net assets, end of period (in 000's)................. $  339,029     $  319,282     $  455,849     $  391,336     $  399,092
Ratio of net expenses to average net assets..........       1.95%          1.83%          1.80%          1.84%          1.82%
Ratio of total expenses to average net assets
   excluding interest expense and fees on loan.......       1.54%          1.49%          1.53%          1.55%          1.52%
Ratio of net investment income (loss) to average
   net assets........................................       1.14%          1.47%          0.88%          0.95%          1.21%
Portfolio turnover rate..............................         72%            42%            42%            54%            46%
INDEBTEDNESS:
Total loan outstanding (in 000's).................... $  121,500     $  110,500     $  158,000     $  145,900     $  141,900
Asset coverage per $1,000 of indebtedness (c)........ $    3,790     $    3,889     $    3,885     $    3,682     $    3,812


-----------------------------

(a)   During the years ended November 30, 2016, 2013 and 2012, the Fund received
      a reimbursement from the sub-advisor in the amount of $1,600, $5,421 and
      $104, respectively, in connection with trade errors, which represent less
      than $0.01 per share. Since the sub-advisor reimbursed the Fund, there was
      no effect on the total return.

(b)   Total return is based on the combination of reinvested dividend, capital
      gain and return of capital distributions, if any, at prices obtained by
      the Dividend Reinvestment Plan, and changes in net asset value per share
      for net asset value returns and changes in Common Share Price for market
      value returns. Total returns do not reflect sales load and are not
      annualized for periods of less than one year. Past performance is not
      indicative of future results.

(c)   Calculated by taking the Fund's total assets less the Fund's total
      liabilities (not including the loan outstanding) and dividing by the
      outstanding loan balance in 000's.


Page 14                 See Notes to Financial Statements





--------------------------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                               NOVEMBER 30, 2016

                                1. ORGANIZATION

First Trust Energy Infrastructure Fund (the "Fund") is a non-diversified,
closed-end management investment company organized as a Massachusetts business
trust on February 22, 2011 and is registered with the Securities and Exchange
Commission (the "SEC") under the Investment Company Act of 1940, as amended (the
"1940 Act"). The Fund trades under the ticker symbol FIF on the New York Stock
Exchange ("NYSE").

The Fund's investment objective is to seek a high level of total return with an
emphasis on current distributions paid to shareholders. The Fund seeks to
achieve its objective by investing primarily in securities of companies engaged
in the energy infrastructure sector. Energy infrastructure companies principally
include publicly-traded master limited partnerships and limited liability
companies taxed as partnerships ("MLPs"), MLP affiliates, YieldCos, pipeline
companies, utilities, and other companies that derive at least 50% of their
revenues from operating or providing services in support of infrastructure
assets such as pipelines, power transmission and petroleum and natural gas
storage in the petroleum, natural gas and power generation industries
(collectively, "Energy Infrastructure Companies"). For purposes of the Fund's
investment objective, total return includes capital appreciation of, and all
distributions received from, securities in which the Fund will invest, taking
into account the varying tax characteristics of such securities. There can be no
assurance that the Fund will achieve its investment objective. The Fund may not
be appropriate for all investors.

                         2. MANAGED DISTRIBUTION POLICY

The Board of Trustees of the Fund has approved a managed distribution policy for
the Fund (the "Plan") in reliance on exemptive relief received from the
Securities and Exchange Commission that permits the Fund to make periodic
distributions of long-term capital gains as frequently as monthly each tax year.
Under the Plan, the Fund currently intends to continue to pay a recurring
monthly distribution in the amount of $0.11 per Common Share that reflects the
distributable cash flow of the Fund. A portion of this monthly distribution may
include realized capital gains. This may result in a reduction of the long-term
capital gain distribution necessary at year end by distributing realized capital
gains throughout the year. The annual distribution rate is independent of the
Fund's performance during any particular period. Accordingly, you should not
draw any conclusions about the Fund's investment performance from the amount of
any distribution or from the terms of the Plan. The Board of Trustees may amend
or terminate the Plan at any time without prior notice to shareholders.

                       3. SIGNIFICANT ACCOUNTING POLICIES

The Fund is considered an investment company and follows accounting and
reporting guidance under Financial Accounting Standards Board Accounting
Standards Codification Topic 946, "Financial Services-Investment Companies." The
following is a summary of significant accounting policies consistently followed
by the Fund in the preparation of its financial statements. The preparation of
financial statements in accordance with accounting principles generally accepted
in the United States of America ("U.S. GAAP") requires management to make
estimates and assumptions that affect the reported amounts and disclosures in
the financial statements. Actual results could differ from those estimates.

A. PORTFOLIO VALUATION

The net asset value ("NAV") of the Common Shares of the Fund is determined daily
as of the close of regular trading on the NYSE, normally 4:00 p.m. Eastern time,
on each day the NYSE is open for trading. If the NYSE closes early on a
valuation day, the NAV is determined as of that time. Foreign securities are
priced using data reflecting the earlier closing of the principal markets for
those securities. The Fund's NAV per Common Share is calculated by dividing the
value of all assets of the Fund (including accrued interest and dividends), less
all liabilities (including accrued expenses, dividends declared but unpaid and
any borrowings of the Fund) by the total number of Common Shares outstanding.

The Fund's investments are valued daily at market value or, in the absence of
market value with respect to any portfolio securities, at fair value. Market
value prices represent last sale or official closing prices from a national or
foreign exchange (i.e., a regulated market) and are primarily obtained from
third-party pricing services. Fair value prices represent any prices not
considered market value prices and are either obtained from a third-party
pricing service or are determined by the Pricing Committee of the Fund's
investment advisor, First Trust Advisors L.P. ("First Trust" or the "Advisor"),
in accordance with valuation procedures adopted by the Fund's Board of Trustees,
and in accordance with provisions of the 1940 Act. Investments valued by the
Advisor's Pricing Committee, if any, are footnoted as such in the footnotes to
the Portfolio of Investments. The Fund's investments are valued as follows:

      Common stocks, MLPs, real estate investment trusts ("REITs"), and other
      equity securities listed on any national or foreign exchange (excluding
      The Nasdaq Stock Market LLC ("Nasdaq") and the London Stock Exchange
      Alternative Investment Market ("AIM")) are valued at the last sale price
      on the exchange on which they are principally traded, or for Nasdaq and
      AIM securities, the official closing price. Securities traded on more than
      one securities exchange are valued at the last sale price or official
      closing price, as applicable, at the close of the securities exchange
      representing the principal market for such securities.

      Exchange-traded options contracts are valued at the closing price in the
      market where such contracts are principally traded. If no closing price is
      available, exchange-traded options contracts are fair valued at the mean
      of their most recent bid and asked price, if available, and otherwise at
      their closing bid price. Over-the-counter options contracts are fair
      valued at the mean of their most recent bid and asked price, if available,
      and otherwise their closing bid price.


                                                                         Page 15





--------------------------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                               NOVEMBER 30, 2016

      Securities traded in an over-the-counter market are fair valued at the
      mean of their most recent bid and asked price, if available, and otherwise
      at their closing bid price.

      Swaps are fair valued utilizing quotations provided by a third-party
      pricing service or, if the pricing service does not provide a value, by
      quotes provided by the selling dealer or financial institution.

Certain securities may not be able to be priced by pre-established pricing
methods. Such securities may be valued by the Fund's Board of Trustees or its
delegate, the Advisor's Pricing Committee, at fair value. These securities
generally include, but are not limited to, restricted securities (securities
which may not be publicly sold without registration under the Securities Act of
1933, as amended (the "1933 Act")) for which a third-party pricing service is
unable to provide a market price; securities whose trading has been formally
suspended; a security whose market or fair value price is not available from a
pre-established pricing source; a security with respect to which an event has
occurred that is likely to materially affect the value of the security after the
market has closed but before the calculation of the Fund's NAV or make it
difficult or impossible to obtain a reliable market quotation; and a security
whose price, as provided by the third-party pricing service, does not reflect
the security's fair value. As a general principle, the current fair value of a
security would appear to be the amount which the owner might reasonably expect
to receive for the security upon its current sale. When fair value prices are
used, generally they will differ from market quotations or official closing
prices on the applicable exchanges. A variety of factors may be considered in
determining the fair value of such securities, including, but not limited to,
the following:

      1)    the type of security;

      2)    the size of the holding;

      3)    the initial cost of the security;

      4)    transactions in comparable securities;

      5)    price quotes from dealers and/or third-party pricing services;

      6)    relationships among various securities;

      7)    information obtained by contacting the issuer, analysts, or the
            appropriate stock exchange;

      8)    an analysis of the issuer's financial statements; and

      9)    the existence of merger proposals or tender offers that might affect
            the value of the security.

If the securities in question are foreign securities, the following additional
information may be considered:

      1)    the value of similar foreign securities traded on other foreign
            markets;

      2)    ADR trading of similar securities;

      3)    closed-end fund trading of similar securities;

      4)    foreign currency exchange activity;

      5)    the trading prices of financial products that are tied to baskets of
            foreign securities;

      6)    factors relating to the event that precipitated the pricing problem;

      7)    whether the event is likely to recur; and

      8)    whether the effects of the event are isolated or whether they affect
            entire markets, countries or regions.

The Fund is subject to fair value accounting standards that define fair value,
establish the framework for measuring fair value and provide a three-level
hierarchy for fair valuation based upon the inputs to the valuation as of the
measurement date. The three levels of the fair value hierarchy are as follows:

      o     Level 1 - Level 1 inputs are quoted prices in active markets for
            identical investments. An active market is a market in which
            transactions for the investment occur with sufficient frequency and
            volume to provide pricing information on an ongoing basis.

      o     Level 2 - Level 2 inputs are observable inputs, either directly or
            indirectly, and include the following:

            o     Quoted prices for similar investments in active markets.

            o     Quoted prices for identical or similar investments in markets
                  that are non-active. A non-active market is a market where
                  there are few transactions for the investment, the prices are
                  not current, or price quotations vary substantially either
                  over time or among market makers, or in which little
                  information is released publicly.

            o     Inputs other than quoted prices that are observable for the
                  investment (for example, interest rates and yield curves
                  observable at commonly quoted intervals, volatilities,
                  prepayment speeds, loss severities, credit risks, and default
                  rates).

            o     Inputs that are derived principally from or corroborated by
                  observable market data by correlation or other means.

      o     Level 3 - Level 3 inputs are unobservable inputs. Unobservable
            inputs may reflect the reporting entity's own assumptions about the
            assumptions that market participants would use in pricing the
            investment.

The inputs or methodologies used for valuing investments are not necessarily an
indication of the risk associated with investing in those investments. A summary
of the inputs used to value the Fund's investments as of November 30, 2016, is
included with the Fund's Portfolio of Investments.


Page 16





--------------------------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                               NOVEMBER 30, 2016


B. OPTION CONTRACTS

The Fund is subject to equity price risk in the normal course of pursuing its
investment objective and may write (sell) options to hedge against changes in
the value of equities. Also, the Fund seeks to generate additional income, in
the form of premiums received, from writing (selling) the options. The Fund may
write (sell) covered call or put options ("options") on all or a portion of the
common stock and MLPs held in the Fund's portfolio as determined to be
appropriate by Energy Income Partners, LLC ("EIP" or the "Sub-Advisor"). The
number of options the Fund can write (sell) is limited by the amount of common
stock and MLPs the Fund holds in its portfolio. The Fund will not write (sell)
"naked" or uncovered options. When the Fund writes (sells) an option, an amount
equal to the premium recived by the Fund is included in "Options written, at
value" on the Fund's Statement of Assets and Liabilities. Options are
marked-to-market daily and their value will be affected by changes in the value
and dividend rates of the underlying equity securities, changes in interest
rates, changes in the actual or perceived volatility of the securities markets
and the underlying equity securities and the remaining time to the options'
expiration. The value of options may also be adversely affected if the market
for the options becomes less liquid or trading volume diminishes.

Options the Fund writes (sells) will either be exercised, expire or be cancelled
pursuant to a closing transaction. If the price of the underlying equity
security exceeds the option's exercise price, it is likely that the option
holder will exercise the option. If an option written (sold) by the Fund is
exercised, the Fund would be obligated to deliver the underlying equity security
to the option holder upon payment of the strike price. In this case, the option
premium received by the Fund will be added to the amount realized on the sale of
the underlying security for purposes of determining gain or loss and is included
in "Net realized gain (loss) on investments" on the Statement of Operations. If
the price of the underlying equity security is less than the option's strike
price, the option will likely expire without being exercised. The option premium
received by the Fund will, in this case, be treated as short-term capital gain
on the expiration date of the option. The Fund may also elect to close out its
position in an option prior to its expiration by purchasing an option of the
same series as the option written (sold) by the Fund. Gain or loss on options is
presented separately as "Net realized gain (loss) on written options" on the
Statement of Operations.

The options that the Fund writes (sells) give the option holder the right, but
not the obligation, to purchase a security from the Fund at the strike price on
or prior to the option's expiration date. The ability to successfully implement
the writing (selling) of covered call options depends on the ability of the
Sub-Advisor to predict pertinent market movements, which cannot be assured.
Thus, the use of options may require the Fund to sell portfolio securities at
inopportune times or for prices other than current market value, which may limit
the amount of appreciation the Fund can realize on an investment, or may cause
the Fund to hold a security that it might otherwise sell. As the writer (seller)
of a covered option, the Fund foregoes, during the option's life, the
opportunity to profit from increases in the market value of the security
covering the option above the sum of the premium and the strike price of the
option, but has retained the risk of loss should the price of the underlying
security decline. The writer (seller) of an option has no control over the time
when it may be required to fulfill its obligation as a writer (seller) of the
option. Once an option writer (seller) has received an exercise notice, it
cannot effect a closing purchase transaction in order to terminate its
obligation under the option and must deliver the underlying security to the
option holder at the exercise price.

Over-the-counter options have the risk of the potential inability of
counterparties to meet the terms of their contracts. The Fund's maximum equity
price risk for purchased options is limited to the premium initially paid. In
addition, certain risks may arise upon entering into option contracts including
the risk that an illiquid secondary market will limit the Fund's ability to
close out an option contract prior to the expiration date and that a change in
the value of the option contract may not correlate exactly with changes in the
value of the securities hedged.

C. SWAP AGREEMENTS

The Fund may enter into total return equity swap and interest rate swap
agreements. A swap is a financial instrument that typically involves the
exchange of cash flows between two parties ("Counterparties") on specified dates
(settlement dates) where the cash flows are based on agreed upon prices, rates,
etc. Payment received or made by the Fund for interest rate swaps are recorded
on the Statement of Operations as "Net realized gain (loss) on swap contracts."
When an interest rate swap is terminated, the Fund will record a realized gain
or loss equal to the difference between the proceeds from (or cost of) the
closing transaction and the Fund's basis in the contract, if any. Generally, the
basis of the contracts, if any, is the premium received or paid. Swap agreements
are individually negotiated and involve the risk of the potential inability of
the Counterparties to meet the terms of the agreement. In connection with these
agreements, cash and securities may be identified as collateral in accordance
with the terms of the respective swap agreements to provide assets of value and
recourse in the event of default under the swap agreement or
bankruptcy/insolvency of a party to the swap agreement. In the event of a
default by a Counterparty, the Fund will seek withdrawal of the collateral and
may incur certain costs exercising its rights with respect to the collateral. If
a Counterparty becomes bankrupt or otherwise fails to perform its obligations
due to financial difficulties, the Fund may experience significant delays in
obtaining any recovery in a bankruptcy or other reorganization proceeding. The
Fund may obtain only limited recovery or may obtain no recovery in such
circumstances.

Swap agreements may increase or decrease the overall volatility of the
investments of the Fund. The performance of swap agreements may be affected by
changes in the specific interest rate, security, currency, or other factors that
determine the amounts of payments due to and from the Fund. The Fund's maximum
equity price risk to meet its future payments under swap agreements outstanding
at November 30, 2016 is equal to the total notional amount as shown on the
Portfolio of Investments. The notional amount represents the U.S. dollar value
of the contract as of the day of the opening transaction or contract reset. When
the Fund enters into a swap agreement, any premium paid is included in "Swap
contracts, at value" on the Statement of Assets and Liabilities.


                                                                         Page 17





--------------------------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                               NOVEMBER 30, 2016

The Fund held interest rate swap agreements at November 30, 2016 to hedge
against changes in borrowing rates under the Fund's committed facility
agreement. An interest rate swap agreement involves the Fund's agreement to
exchange a stream of interest payments for another party's stream of cash flows.
Interest rate swaps do not involve the delivery of securities or other
underlying assets or principal. Accordingly, the risk of loss with respect to
interest rate swaps is limited to the net amount of interest payments that the
Fund is contractually obligated to make. Cash segregated as collateral for open
swap contracts in the amount of $5,664,059 is shown on the Statement of Assets
and Liabilities.

D. SECURITIES TRANSACTIONS AND INVESTMENT INCOME

Securities transactions are recorded as of the trade date. Realized gains and
losses from securities transactions are recorded on the identified cost basis.
Dividend income is recorded on the ex-dividend date. Interest income is recorded
daily on the accrual basis. The Fund will rely to some extent on information
provided by MLPs, which is not necessarily timely, to estimate taxable income
allocable to the MLP units held in the Fund's portfolio.

Distributions received from the Fund's investments in MLPs generally are
comprised of return of capital and investment income. The Fund records estimated
return of capital and investment income based on historical information
available from each MLP. These estimates may subsequently be revised based on
information received from the MLPs after their tax reporting periods are
concluded. For the year ended November 30, 2016, distributions of $8,187,381
received from MLPs have been reclassified as return of capital. The cost basis
of applicable MLPs has been reduced accordingly.

The Fund holds shares of REITs. Distributions from such investments may be
comprised of return of capital, capital gains and income. The actual character
of amounts received during the year is not known until after the REIT's fiscal
year end. The Fund records the character of distributions received from REITs
during the year based on estimates available. The characterization of
distributions received by the Fund may be subsequently revised based on
information received from the REITs after their tax reporting periods conclude.

E. DIVIDENDS AND DISTRIBUTIONS TO SHAREHOLDERS

The Fund intends to pay holders of its Common Shares a recurring monthly
distribution that reflects the distributable cash flow of the Fund.
Distributions will automatically be reinvested into additional Common Shares
pursuant to the Fund's Dividend Reinvestment Plan unless cash distributions are
elected by the shareholder.

Distributions from income and capital gains are determined in accordance with
federal income tax regulations, which may differ from U.S. GAAP. Certain capital
accounts in the financial statements are periodically adjusted for permanent
differences in order to reflect their tax character. These permanent differences
are primarily due to the varying treatment of income and gain/loss on portfolio
securities held by the Fund and have no impact on net assets or NAV per Common
Share. Temporary differences, which arise from recognizing certain items of
income, expense and gain/loss in different periods for financial statement and
tax purposes, will reverse at some point in the future. Permanent differences
incurred during the year ended November 30, 2016, primarily as a result of
differing book and tax treatments on the sale of MLP investments, have been
reclassified at year end to reflect a decrease in accumulated net investment
income (loss) of $2,630,476, an increase in accumulated net realized gain (loss)
on investments of $2,668,887 and a decrease to paid-in capital of $38,411. Net
assets were not affected by these reclassifications.

The tax character of distributions paid during the fiscal years ended November
30, 2016 and 2015 is as follows:

Distributions paid from:                                 2016            2015
Ordinary income...................................  $  3,981,810    $  9,729,196
Capital gain......................................     5,326,861      13,437,116
Return of capital.................................    19,824,721              --

As of November 30, 2016, the components of distributable earnings and net assets
on a tax basis were as follows:

Undistributed ordinary income.....................  $         --
Undistributed capital gains.......................            --
                                                    ------------
Total undistributed earnings......................            --
Accumulated capital and other losses..............    (7,301,850)
Net unrealized appreciation (depreciation)........    33,903,845
                                                    ------------
Total accumulated earnings (losses)...............    26,601,995
Other.............................................       (53,352)
Paid-in capital...................................   312,480,673
                                                    ------------
Net assets........................................  $339,029,316
                                                    ============


Page 18





--------------------------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                               NOVEMBER 30, 2016


F. INCOME TAXES

The Fund intends to continue to qualify as a regulated investment company by
complying with the requirements under Subchapter M of the Internal Revenue Code
of 1986, as amended, which includes distributing substantially all of its net
investment income and net realized gains to shareholders. Accordingly, no
provision has been made for federal and state income taxes. However, due to the
timing and amount of distributions, the Fund may be subject to an excise tax of
4% of the amount by which approximately 98% of the Fund's taxable income exceeds
the distributions from such taxable income for the calendar year.

The Fund intends to utilize provisions of the federal income tax laws, which
allow it to carry a realized capital loss forward indefinitely following the
year of the loss and offset such loss against any future realized capital gains.
The Fund is subject to certain limitations under U.S. tax rules on the use of
capital loss carryforwards and net unrealized built-in losses. These limitations
apply when there has been a 50% change in ownership. At November 30, 2016, the
Fund had capital loss carryforwards for federal income tax purposes of
$7,301,850.

Certain losses realized during the current fiscal year may be deferred and
treated as occurring on the first day of the following fiscal year for federal
income tax purposes. For the fiscal year ended November 30, 2016, the Fund had
no qualified late year losses.

The Fund is subject to accounting standards that establish a minimum threshold
for recognizing, and a system for measuring, the benefits of a tax position
taken or expected to be taken in a tax return. Taxable years ending 2013, 2014,
2015 and 2016 remain open to federal and state audit. As of November 30, 2016,
management has evaluated the application of these standards to the Fund and has
determined that no provision for income tax is required in the Fund's financial
statements for uncertain tax positions.

G. EXPENSES

The Fund will pay all expenses directly related to its operations.

H. FOREIGN CURRENCY

The books and records of the Fund are maintained in U.S. dollars. Foreign
currencies, investments and other assets and liabilities are translated into
U.S. dollars at the exchange rates prevailing at the end of the period.
Purchases and sales of investments and items of income and expense are
translated on the respective dates of such transactions. Unrealized gains and
losses on assets and liabilities, other than investments in securities, which
result from changes in foreign currency exchange rates have been included in
"Net change in unrealized appreciation (depreciation) on foreign currency
translation" on the Statement of Operations. Unrealized gains and losses on
investments in securities which result from changes in foreign exchange rates
are included with fluctuations arising from changes in market price and are
shown in "Net change in unrealized appreciation (depreciation) on investments"
on the Statement of Operations. Net realized foreign currency gains and losses
include the effect of changes in exchange rates between trade date and
settlement date on investment security transactions, foreign currency
transactions and interest and dividends received and are shown in "Net realized
gain (loss) on foreign currency transactions" on the Statement of Operations.
The portion of foreign currency gains and losses related to fluctuation in
exchange rates between the initial purchase settlement date and subsequent sale
trade date is included in "Net realized gain (loss) on investments" on the
Statement of Operations.

I. OFFSETTING ON THE STATEMENT OF ASSETS AND LIABILITIES

Offsetting assets and liabilities require entities to disclose both gross and
net information about instruments and transactions eligible for offset on the
Statements of Assets and Liabilities, and disclose instruments and transactions
subject to master netting or similar agreements. These disclosure requirements
are intended to help investors and other financial statement users better assess
the effect or potential effect of offsetting arrangements on a fund's financial
position. The transactions subject to offsetting disclosures are derivative
instruments, repurchase agreements and reverse repurchase agreements, and
securities borrowing and securities lending transactions.

For financial reporting purposes, the Fund does not offset financial assets and
financial liabilities that are subject to master netting arrangements ("MNAs")
or similar agreements on the Statement of Assets and Liabilities. MNAs provide
the right, in the event of default (including bankruptcy and insolvency), for
the non-defaulting counterparty to liquidate the collateral and calculate the
net exposure to the defaulting party or request additional collateral.

At November 30, 2016, derivative assets and liabilities (by type) on a gross
basis are as follows:



                                                                                         GROSS AMOUNTS NOT OFFSET
                                                                                           IN THE STATEMENT OF
                                                                    NET AMOUNTS OF        ASSETS AND LIABILITIES
                                 GROSS         GROSS AMOUNTS     LIABILITIES PRESENTED  --------------------------
                               AMOUNTS OF      OFFSET IN THE       IN THE STATEMENT                      CASH
                               RECOGNIZED   STATEMENT OF ASSETS      OF ASSETS AND       FINANCIAL   SEGREGATED AS      NET
                              LIABILITIES     AND LIABILITIES         LIABILITIES       INSTRUMENTS   COLLATERAL      AMOUNT
-------------------------------------------------------------------------------------------------------------------------------
                                                                                                    
Interest Rate Swap Contracts  $ (2,150,883)       $    --           $ (2,150,883)          $    --    $ 2,150,883     $    --



                                                                         Page 19





--------------------------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                               NOVEMBER 30, 2016


J. NEW AND AMENDED FINANCIAL REPORTING RULES AND FORMS

On October 13, 2016 the SEC adopted new rules and forms, and amended existing
rules and forms. The new and amended rules and forms are intended to modernize
the reporting of information provided by funds and to improve the quality and
type of information that funds provide to the SEC and investors. The new and
amended rules and forms will be effective for the First Trust funds, including
the Fund, for reporting periods beginning on and after June 1, 2018. Management
is evaluating the new and amended rules and forms to determine the impact to the
Fund.

 4. INVESTMENT ADVISORY FEE, AFFILIATED TRANSACTIONS AND OTHER FEE ARRANGEMENTS

First Trust, the investment advisor to the Fund, is a limited partnership with
one limited partner, Grace Partners of DuPage L.P., and one general partner, The
Charger Corporation. The Charger Corporation is an Illinois corporation
controlled by James A. Bowen, Chief Executive Officer of First Trust. First
Trust is responsible for the ongoing monitoring of the Fund's investment
portfolio, managing the Fund's business affairs and providing certain
administrative services necessary for the management of the Fund. For these
investment management services, First Trust is entitled to a monthly fee
calculated at an annual rate of 1.00% of the Fund's Managed Assets (the average
daily total asset value of the Fund minus the sum of the Fund's liabilities
other than the principal amount of borrowings). First Trust also provides fund
reporting services to the Fund for a flat annual fee in the amount of $9,250.

EIP serves as the Fund's sub-advisor and manages the Fund's portfolio subject to
First Trust's supervision. The Sub-Advisor receives a monthly sub-advisory fee
calculated at an annual rate of 0.50% of the Fund's Managed Assets that is paid
by First Trust out of its investment advisory fee.

During the year ended November 30, 2016, the Fund received a payment from the
Sub-Advisor of $1,600 in connection with a trade error.

First Trust Capital Partners, LLC, an affiliate of First Trust, owns, through a
wholly-owned subsidiary, a 15% ownership interest in each of EIP and EIP
Partners, LLC, an affiliate of the EIP.

BNY Mellon Investment Servicing (US) Inc. ("BNYM IS") serves as the Fund's
administrator, fund accountant and transfer agent in accordance with certain fee
arrangements. As administrator and fund accountant, BNYM IS is responsible for
providing certain administrative and accounting services to the Fund, including
maintaining the Fund's books of account, records of the Fund's securities
transactions, and certain other books and records. As transfer agent, BNYM IS is
responsible for maintaining shareholder records for the Fund. The Bank of New
York Mellon ("BNYM") serves as the Fund's custodian in accordance with certain
fee arrangements. As custodian, BNYM is responsible for custody of the Fund's
assets. BNYM IS and BNYM are subsidiaries of The Bank of New York Mellon
Corporation, a financial holding company.

Each Trustee who is not an officer or employee of First Trust, any sub-advisor
or any of their affiliates ("Independent Trustees") is paid a fixed annual
retainer that is allocated equally among each fund in the First Trust Fund
Complex. Prior to January 1, 2016, the fixed annual retainer was allocated pro
rata based on each fund's net assets. Each Independent Trustee is also paid an
annual per fund fee that varies based on whether the fund is a closed-end or
other actively managed fund, or is an index fund.

Additionally, the Lead Independent Trustee and the Chairmen of the Audit
Committee, Nominating and Governance Committee and Valuation Committee are paid
annual fees to serve in such capacities, with such compensation allocated pro
rata among each fund in the First Trust Fund Complex based on net assets.
Independent Trustees are reimbursed for travel and out-of-pocket expenses in
connection with all meetings. The Lead Independent Trustee and Committee
Chairmen rotate every three years. The officers and "Interested" Trustee receive
no compensation from the Fund for acting in such capacities.

                      5. PURCHASES AND SALES OF SECURITIES

Cost of purchases and proceeds from sales of investments, excluding short-term
investments, for the year ended November 30, 2016, were $291,796,579 and
$301,599,948, respectively.


Page 20





--------------------------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                               NOVEMBER 30, 2016

                           6. DERIVATIVE TRANSACTIONS

Written option activity for the Fund was as follows:


                                                    NUMBER OF
WRITTEN OPTIONS                                     CONTRACTS      PREMIUMS
-----------------------------------------------------------------------------
Options outstanding at November 30, 2015.........      25,130    $  1,352,376
Options Written..................................     135,240       7,330,129
Options Expired..................................     (71,730)     (3,621,493)
Options Exercised................................     (42,451)     (2,358,943)
Options Closed...................................     (22,389)     (1,334,884)
                                                    ---------    ------------
Options outstanding at November 30, 2016.........      23,800    $  1,367,185
                                                    =========    ============

The following table presents the types of derivatives held by the Fund at
November 30, 2016, the primary underlying risk exposure and the location of
these instruments as presented on the Statement of Assets and Liabilities.



                                                   ASSET DERIVATIVES                      LIABILITY DERIVATIVES
                                        ---------------------------------------  ---------------------------------------
    DERIVATIVE             RISK          STATEMENT OF ASSETS AND                  STATEMENT OF ASSETS AND
   INSTRUMENTS           EXPOSURE         LIABILITIES LOCATION        VALUE        LIABILITIES LOCATION        VALUE
------------------  ------------------  -------------------------  ------------  -------------------------  ------------
                                                                                             
Written Options     Equity Risk                     --                  --       Options written, at value  $  1,485,850
Interest Rate Swap
  Agreement         Interest Rate Risk              --                  --       Swap contracts, at value      2,150,883


The following table presents the amount of net realized gain (loss) and change
in net unrealized appreciation (depreciation) recognized for the year ended
November 30, 2016, on derivative instruments, as well as the primary underlying
risk exposure associated with each instrument.

STATEMENT OF OPERATIONS LOCATION
------------------------------------------------------------------------
EQUITY RISK EXPOSURE
Net realized gain (loss) on written options                  $  (104,215)

Net change in unrealized appreciation
   (depreciation) on written options                            (765,736)

INTEREST RATE RISK EXPOSURE
Net realized gain (loss) on swap contracts                    (1,339,446)

Net change in unrealized appreciation
   (depreciation) on swap contracts                              786,229

The average volume of interest rate swaps was $72,950,000 for the year ended
November 30, 2016.

The Fund does not have the right to offset financial assets and financial
liabilities related to option contracts on the Statement of Assets and
Liabilities.

                                 7. BORROWINGS

The Fund has a committed facility agreement with The Bank of Nova Scotia
("Scotia"). Effective March 1, 2016, the committed facility agreement was
amended. The maximum commitment amount was reduced to $130,000,000 from
$200,000,000. In addition, the borrowing rate was increased to the 1-month LIBOR
plus 85 basis points from the 1-month LIBOR plus 70 basis points. Under the
facility, the Fund pays a commitment fee of 0.15% when the undrawn amount of
such facility is greater than 50% of the maximum commitment. The average amount
outstanding under the facility for the fiscal year ended November 30, 2016 was
$109,808,743, with a weighted average interest rate of 1.29%. As of November 30,
2016, the Fund had outstanding borrowings of $121,500,000 under this committed
facility agreement. The high and low annual interest rates for the fiscal year
ended November 30, 2016, were 1.47% and 0.94%, respectively. The interest rate
at November 30, 2016 was 1.47%.

                               8. INDEMNIFICATION

The Fund has a variety of indemnification obligations under contracts with its
service providers. The Fund's maximum exposure under these arrangements is
unknown. However, the Fund has not had prior claims or losses pursuant to these
contracts and expects the risk of loss to be remote.


                                                                         Page 21





--------------------------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                               NOVEMBER 30, 2016

                         9. INDUSTRY CONCENTRATION RISK

The Fund invests at least 80% of its Managed Assets in securities issued by
Energy Infrastructure Companies. Given this industry concentration, the Fund is
more susceptible to adverse economic or regulatory occurrences affecting that
industry than an investment company that is not concentrated in a single
industry. Energy Infrastructure Company issuers may be subject to a variety of
factors that may adversely affect their business or operations, including high
interest costs in connection with capital construction programs, high leverage
costs associated with environmental and other regulations, the effects of
economic slowdown, surplus capacity, increased competition from other providers
of services, uncertainties concerning the availability of fuel at reasonable
prices, the effects of energy conservation policies and other factors.

               10. NON-FUNDAMENTAL CHANGE IN INVESTMENT STRATEGY

On February 1, 2016, the Board of Trustees for the Fund approved the following
non-fundamental change to the Fund's investment strategy:

      The Fund's covered call limit was increased from 30% to 35%. Accordingly,
      effective on or about April 11, 2016, the Fund may write (or sell) covered
      call options on up to 35% of its Managed Assets.

The Fund's investment objective did not change.

                             11. SUBSEQUENT EVENTS

Management has evaluated the impact of all subsequent events to the Fund through
the date the financial statements were issued and has determined that there was
the following subsequent event:

On December 20, 2016, the Fund declared a distribution of $0.11 per share to
Common Shareholders of record on January 5, 2017, payable January 17, 2017.


Page 22





--------------------------------------------------------------------------------
REPORT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM
--------------------------------------------------------------------------------

TO THE BOARD OF TRUSTEES AND SHAREHOLDERS OF FIRST TRUST ENERGY INFRASTRUCTURE
FUND:

We have audited the accompanying statement of assets and liabilities of First
Trust Energy Infrastructure Fund (the "Fund"), including the portfolio of
investments, as of November 30, 2016, and the related statements of operations
and cash flows for the year then ended, the statements of changes in net assets
for each of the two years in the period then ended, and the financial highlights
for each of the five years in the period then ended. These financial statements
and financial highlights are the responsibility of the Fund's management. Our
responsibility is to express an opinion on these financial statements and
financial highlights based on our audits.

We conducted our audits in accordance with the standards of the Public Company
Accounting Oversight Board (United States). Those standards require that we plan
and perform the audit to obtain reasonable assurance about whether the financial
statements and financial highlights are free of material misstatement. The Fund
is not required to have, nor were we engaged to perform, an audit of its
internal control over financial reporting. Our audits included consideration of
internal control over financial reporting as a basis for designing audit
procedures that are appropriate in the circumstances, but not for the purpose of
expressing an opinion on the effectiveness of the Fund's internal control over
financial reporting. Accordingly, we express no such opinion. An audit also
includes examining, on a test basis, evidence supporting the amounts and
disclosures in the financial statements, assessing the accounting principles
used and significant estimates made by management, as well as evaluating the
overall financial statement presentation. Our procedures included confirmation
of securities owned as of November 30, 2016 by correspondence with the Fund's
custodian and brokers; where replies were not received from brokers, we
performed other auditing procedures. We believe that our audits provide a
reasonable basis for our opinion.

In our opinion, the financial statements and financial highlights referred to
above present fairly, in all material respects, the financial position of First
Trust Energy Infrastructure Fund, as of November 30, 2016, the results of its
operations and its cash flows for the year then ended, the changes in its net
assets for each of the two years in the period then ended, and the financial
highlights for each of the five years in the period then ended, in conformity
with accounting principles generally accepted in the United States of America.

/s/ Deloitte & Touche LLP

Chicago, Illinois
January 24, 2017


                                                                         Page 23





--------------------------------------------------------------------------------
ADDITIONAL INFORMATION
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                         NOVEMBER 30, 2016 (UNAUDITED)

                           DIVIDEND REINVESTMENT PLAN

If your Common Shares are registered directly with the Fund or if you hold your
Common Shares with a brokerage firm that participates in the Fund's Dividend
Reinvestment Plan (the "Plan"), unless you elect, by written notice to the Fund,
to receive cash distributions, all dividends, including any capital gain
distributions, on your Common Shares will be automatically reinvested by BNY
Mellon Investment Servicing (US) Inc. (the "Plan Agent"), in additional Common
Shares under the Plan. If you elect to receive cash distributions, you will
receive all distributions in cash paid by check mailed directly to you by the
Plan Agent, as the dividend paying agent.

If you decide to participate in the Plan, the number of Common Shares you will
receive will be determined as follows:

      (1)   If Common Shares are trading at or above net asset value ("NAV") at
            the time of valuation, the Fund will issue new shares at a price
            equal to the greater of (i) NAV per Common Share on that date or
            (ii) 95% of the market price on that date.

      (2)   If Common Shares are trading below NAV at the time of valuation, the
            Plan Agent will receive the dividend or distribution in cash and
            will purchase Common Shares in the open market, on the NYSE or
            elsewhere, for the participants' accounts. It is possible that the
            market price for the Common Shares may increase before the Plan
            Agent has completed its purchases. Therefore, the average purchase
            price per share paid by the Plan Agent may exceed the market price
            at the time of valuation, resulting in the purchase of fewer shares
            than if the dividend or distribution had been paid in Common Shares
            issued by the Fund. The Plan Agent will use all dividends and
            distributions received in cash to purchase Common Shares in the open
            market within 30 days of the valuation date except where temporary
            curtailment or suspension of purchases is necessary to comply with
            federal securities laws. Interest will not be paid on any uninvested
            cash payments.

You may elect to opt-out of or withdraw from the Plan at any time by giving
written notice to the Plan Agent, or by telephone at (866) 340-1104, in
accordance with such reasonable requirements as the Plan Agent and the Fund may
agree upon. If you withdraw or the Plan is terminated, you will receive a
certificate for each whole share in your account under the Plan, and you will
receive a cash payment for any fraction of a share in your account. If you wish,
the Plan Agent will sell your shares and send you the proceeds, minus brokerage
commissions.

The Plan Agent maintains all Common Shareholders' accounts in the Plan and gives
written confirmation of all transactions in the accounts, including information
you may need for tax records. Common Shares in your account will be held by the
Plan Agent in non-certificated form. The Plan Agent will forward to each
participant any proxy solicitation material and will vote any shares so held
only in accordance with proxies returned to the Fund. Any proxy you receive will
include all Common Shares you have received under the Plan.

There is no brokerage charge for reinvestment of your dividends or distributions
in Common Shares. However, all participants will pay a pro rata share of
brokerage commissions incurred by the Plan Agent when it makes open market
purchases.

Automatically reinvesting dividends and distributions does not mean that you do
not have to pay income taxes due upon receiving dividends and distributions.
Capital gains and income are realized although cash is not received by you.
Consult your financial advisor for more information.

If you hold your Common Shares with a brokerage firm that does not participate
in the Plan, you will not be able to participate in the Plan and any dividend
reinvestment may be effected on different terms than those described above.

The Fund reserves the right to amend or terminate the Plan if in the judgment of
the Board of Trustees the change is warranted. There is no direct service charge
to participants in the Plan; however, the Fund reserves the right to amend the
Plan to include a service charge payable by the participants. Additional
information about the Plan may be obtained by writing BNY Mellon Investment
Servicing (US) Inc., 301 Bellevue Parkway, Wilmington, Delaware 19809.

--------------------------------------------------------------------------------

                      PROXY VOTING POLICIES AND PROCEDURES

A description of the policies and procedures that the Fund uses to determine how
to vote proxies and information on how the Fund voted proxies relating to
portfolio investments during the most recent 12-month period ended June 30 is
available (1) without charge, upon request, by calling (800) 988-5891; (2) on
the Fund's website located at http://www.ftportfolios.com; and (3) on the
Securities and Exchange Commission's ("SEC") website located at
http://www.sec.gov.


Page 24





--------------------------------------------------------------------------------
ADDITIONAL INFORMATION (CONTINUED)
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                         NOVEMBER 30, 2016 (UNAUDITED)

                               PORTFOLIO HOLDINGS

The Fund files its complete schedule of portfolio holdings with the SEC for the
first and third quarters of each fiscal year on Form N-Q. The Fund's Form N-Qs
are available (1) by calling (800) 988-5891; (2) on the Fund's website located
at http://www.ftportfolios.com; (3) on the SEC's website at http://www.sec.gov;
and (4) for review and copying at the SEC's Public Reference Room ("PRR") in
Washington, DC. Information regarding the operation of the PRR may be obtained
by calling (800) SEC-0330.

                                TAX INFORMATION

Of the ordinary income (including short-term capital gain) distributions made by
the Fund during the fiscal year ended November 30, 2016, 69.75% qualified for
the corporate dividends received deduction available to corporate shareholders.

The Fund hereby designates as qualified dividend income 100.00% of the ordinary
income distributions for the year ended November 30, 2016.

For the fiscal year ended November 30, 2016, the amount of long-term capital
gain distributions by the Fund was $5,326,861 which is taxable at the maximum
rate of 20% for federal income tax purposes.

                         NYSE CERTIFICATION INFORMATION

In accordance with Section 303A-12 of the New York Stock Exchange ("NYSE")
Listed Company Manual, the Fund's President has certified to the NYSE that, as
of April 26, 2016, he was not aware of any violation by the Fund of NYSE
corporate governance listing standards. In addition, the Fund's reports to the
SEC on Forms N-CSR, N-CSRS and N-Q contain certifications by the Fund's
principal executive officer and principal financial officer that relate to the
Fund's public disclosure in such reports and are required by Rule 30a-2 under
the 1940 Act.

                SUBMISSION OF MATTERS TO A VOTE OF SHAREHOLDERS

The Joint Annual Meeting of Shareholders of the Common Shares of Macquarie/First
Trust Global Infrastructure/Utilities Dividend & Income Fund, First Trust Energy
Income and Growth Fund, First Trust Enhanced Equity Income Fund, First
Trust/Aberdeen Global Opportunity Income Fund, First Trust Mortgage Income Fund,
First Trust Strategic High Income Fund II, First Trust/Aberdeen Emerging
Opportunity Fund, First Trust Specialty Finance and Financial Opportunities
Fund, First Trust High Income Long/Short Fund, First Trust Energy Infrastructure
Fund, First Trust MLP and Energy Income Fund, First Trust New Opportunities MLP
& Energy Fund and First Trust Intermediate Duration Preferred & Income Fund was
held on April 22, 2016 (the "Annual Meeting"). At the Annual Meeting, James A.
Bowen and Niel B. Nielson were elected by the Common Shareholders of the First
Trust Energy Infrastructure Fund as a Class III Trustees for a three-year term
expiring at the Fund's Annual Meeting of Shareholders in 2019. The number of
votes cast for Mr. Bowen was 15,200,150, the number of votes against was 254,313
and the number of broker non-votes was 2,095,773. The number of votes cast for
Mr. Nielson was 15,190,444, the number of votes against was 264,019 and the
number of broker non-votes was 2,095,773. Richard E. Erickson, Thomas R. Kadlec,
and Robert F. Keith are the other current and continuing Trustees.

                              RISK CONSIDERATIONS

Risks are inherent in all investing. The following summarizes some, but not all,
of the risks that should be considered for the Fund. For additional information
about the risks associated with investing in the Fund, please see the Fund's
prospectus and statement of additional information, as well as other Fund
regulatory filings.

CURRENCY RISK: The value of securities denominated or quoted in foreign
currencies may be adversely affected by fluctuations in the relative currency
exchange rates and by exchange control regulations. The Fund's investment
performance may be negatively affected by a devaluation of a currency in which
the Fund's investments are denominated or quoted. Further, the Fund's investment
performance may be significantly affected, either positively or negatively, by
currency exchange rates because the U.S. dollar value of securities denominated
or quoted in another currency will increase or decrease in response to changes
in the value of such currency in relation to the U.S. dollar. While certain of
the Fund's non-U.S. dollar-denominated securities may be hedged into U.S.
dollars, hedging may not alleviate all currency risks.

DERIVATIVES RISK: The Fund may enter into total return swaps, credit default
swaps or other types of swaps, options, forwards and combinations thereof and
related derivatives. These transactions generally provide for the transfer from
one counterparty to another of certain risks inherent in the ownership of a
financial asset such as a common stock or debt instrument. Such risks include,
among other things, the risk of default and insolvency of the obligor of such
asset, the risk that the credit of the obligor or the underlying collateral will
decline or the risk that the common stock of the underlying issuer will decline
in value. The Fund's ability to successfully use hedging and interest rate
derivative transactions depends on the Sub-Advisor's ability to predict
pertinent market movements, which cannot be assured. Thus, the use of
derivatives for hedging and interest rate management purposes may result in
losses greater than if they had not been used, may require the Fund to sell or


                                                                         Page 25





--------------------------------------------------------------------------------
ADDITIONAL INFORMATION (CONTINUED)
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                         NOVEMBER 30, 2016 (UNAUDITED)

purchase portfolio securities at inopportune times or for prices other than
current market values, may limit the amount of appreciation the Fund can realize
on an investment, or may cause the Fund to hold a security that it might
otherwise sell. Additionally, amounts paid by the Fund as premiums and cash or
other assets held in margin accounts with respect to hedging and strategic
transactions are not otherwise available to the Fund for investment purposes. As
the writer of a covered call option, the Fund forgoes, during the option's life,
the opportunity to profit from increases in the market value of the security
covering the call option above the sum of the premium and the strike price of
the call, but has retained the risk of loss should the price of the underlying
security decline. The writer of an option has no control over the time when it
may be required to fulfill its obligation as a writer of the option. Once an
option writer has received an exercise notice, it cannot effect a closing
purchase transaction in order to terminate its obligation under the option and
must deliver the underlying security at the exercise price.

ENERGY INFRASTRUCTURE COMPANIES RISK: The Fund invests in Energy Infrastructure
Companies and is subject to certain risks inherent in investing in these types
of securities. Energy Infrastructure Companies may be directly affected by
energy commodity prices, especially those Energy Infrastructure Companies which
own the underlying energy commodity. A decrease in the production or
availability of natural gas, natural gas liquids ("NGLs"), crude oil, coal or
other energy commodities or a decrease in the volume of such commodities
available for transportation, processing, storage or distribution may adversely
impact the financial performance of Energy Infrastructure Companies. Energy
Infrastructure Companies are subject to significant federal, state and local
government regulation in virtually every aspect of their operations, including
how facilities are constructed, maintained and operated, environmental and
safety controls, and the prices they may charge for products and services.
Various governmental authorities have the power to enforce compliance with these
regulations and the permits issued under them and violators are subject to
administrative, civil and criminal penalties, including civil fines, injunctions
or both. Stricter laws, regulations or enforcement policies could be enacted in
the future which would likely increase compliance costs and may adversely affect
the financial performance of Energy Infrastructure Companies. Natural disasters,
such as hurricanes in the Gulf of Mexico, also may impact Energy Infrastructure
Companies.

Certain Energy Infrastructure Companies are subject to the imposition of rate
caps, increased competition due to deregulation, the difficulty in obtaining an
adequate return on invested capital or in financing large construction projects,
the limitations on operations and increased costs and delays attributable to
environmental considerations, and the capital market's ability to absorb utility
debt. In addition, taxes, government regulation, international politics, price
and supply fluctuations, volatile interest rates and energy conservation may
cause difficulties for these companies. Such issuers have been experiencing
certain of these problems to varying degrees.

EQUITY SECURITIES RISK: Because the Fund invests in equity securities, the value
of the Fund's shares will fluctuate with changes in the value of these equity
securities. Equity securities prices fluctuate for several reasons, including
changes in investors' perceptions of the financial condition of an issuer or the
general condition of the relevant stock market, such as market volatility, or
when political or economic events affecting the issuers occur. In addition,
common stock prices may be particularly sensitive to rising interest rates, as
the cost of the capital rises and borrowing costs increase.

INDUSTRY CONCENTRATION RISK: The Fund invests at least 80% of its Managed Assets
in securities issued by Energy Infrastructure Companies. Given this industry
concentration, the Fund is more susceptible to adverse economic or regulatory
occurrences affecting that industry than an investment company that is not
concentrated in a single industry. Energy Infrastructure Company issuers may be
subject to a variety of factors that may adversely affect their business or
operations, including high interest costs in connection with capital
construction programs, high leverage costs associated with environmental and
other regulations, the effects of economic slowdown, surplus capacity, increased
competition from other providers of services, uncertainties concerning the
availability of fuel at reasonable prices, the effects of energy conservation
policies and other factors.

INVESTMENT AND MARKET RISK: An investment in the Fund's Common Shares is subject
to investment risk, including the possible loss of the entire principal
invested. An investment in Common Shares represents an indirect investment in
the securities owned by the Fund. The value of these securities, like other
market investments, may move up or down, sometimes rapidly and unpredictably.
Common Shares at any point in time may be worth less than the original
investment, even after taking into account the reinvestment of Fund dividends
and distributions. Security prices can fluctuate for several reasons including
the general condition of the securities markets, or when political or economic
events affecting the issuers occur. When the Advisor or Sub-Advisor determines
that it is temporarily unable to follow the Fund's investment strategy or that
it is impractical to do so (such as when a market disruption event has occurred
and trading in the securities is extremely limited or absent), the Fund may take
temporary defensive positions.

LEVERAGE RISK: The use of leverage results in additional risks and can magnify
the effect of any losses. The funds borrowed pursuant to a leverage borrowing
program constitute a substantial lien and burden by reason of their prior claim
against the income of the Fund and against the net assets of the Fund in
liquidation. If the Fund is not in compliance with certain credit facility
provisions, the Fund may not be permitted to declare dividends or other
distributions.


Page 26





--------------------------------------------------------------------------------
ADDITIONAL INFORMATION (CONTINUED)
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                         NOVEMBER 30, 2016 (UNAUDITED)

MLP RISK: An investment in MLP units involves risks which differ from an
investment in common stock of a corporation. Holders of MLP units have limited
control and voting rights on matters affecting the partnership. In addition,
there are certain tax risks associated with an investment in MLP units and
conflicts of interest exist between common unit holders and the general partner,
including those arising from incentive distribution payments.

NON-DIVERSIFIED RISK: The Fund is a non-diversified investment company under the
1940 Act and will not be treated as a regulated investment company under the
Internal Revenue Code. Accordingly, there are no regulatory requirements under
the 1940 Act of the Internal Revenue Code on the minimum number or size of
securities held by the Fund.

NON-U.S. RISK: The Fund may invest a portion of its assets in the equity
securities of issuers domiciled in jurisdictions other than the U.S. Investments
in the securities and instruments of non-U.S. issuers involve certain
considerations and risks not ordinarily associated with investments in
securities and instruments of U.S. issuers. Non-U.S. companies are not generally
subject to uniform accounting, auditing and financial standards and requirements
comparable to those applicable to U.S. companies. Non-U.S. securities exchanges,
brokers and listed companies may be subject to less government supervision and
regulation than exists in the United States. Dividend and interest income may be
subject to withholding and other non-U.S. taxes, which may adversely affect the
net return on such investments. A related risk is that there may be difficulty
in obtaining or enforcing a court judgment abroad.

QUALIFIED DIVIDEND INCOME TAX RISK: There can be no assurance as to what portion
of the distributions paid to the Fund's Common Shareholders will consist of
tax-advantaged qualified dividend income. Certain distributions designated by
the Fund as derived from qualified dividend income will be taxed in the hands of
non-corporate Common Shareholders at the rates applicable to long-term capital
gains, provided certain holding period and other requirements are satisfied by
both the Fund and the Common Shareholders. Additional requirements apply in
determining whether distributions by foreign issuers should be regarded as
qualified dividend income. Certain investment strategies of the Fund will limit
the Fund's ability to meet these requirements and consequently will limit the
amount of qualified dividend income received and distributed by the Fund. A
change in the favorable provisions of the federal tax laws with respect to
qualified dividends may result in a widespread reduction in announced dividends
and may adversely impact the valuation of the shares of dividend-paying
companies.

RESTRICTED SECURITIES RISK: The Fund may invest in unregistered or otherwise
restricted securities. The term "restricted securities" refers to securities
that are unregistered or are held by control persons of the issuer and
securities that are subject to contractual restrictions on their resale. As a
result, restricted securities may be more difficult to value and the Fund may
have difficulty disposing of such assets either in a timely manner or for a
reasonable price. In order to dispose of an unregistered security, the Fund,
where it has contractual rights to do so, may have to cause such security to be
registered. A considerable period may elapse between the time the decision is
made to sell the security and the time the security is registered so that the
Fund could sell it. Contractual restrictions on the resale of securities vary in
length and scope and are generally the result of a negotiation between the
issuer and acquirer of the securities. The Fund would, in either case, bear
market risks during that period.

                      ADVISORY AND SUB-ADVISORY AGREEMENTS

BOARD CONSIDERATIONS REGARDING APPROVAL OF INVESTMENT MANAGEMENT AGREEMENT AND
INVESTMENT SUB-ADVISORY AGREEMENT

The Board of Trustees of First Trust Energy Infrastructure Fund (the "Fund"),
including the Independent Trustees, unanimously approved the continuation of the
Investment Management Agreement (the "Advisory Agreement") between the Fund and
First Trust Advisors L.P. (the "Advisor") and the Investment Sub-Advisory
Agreement (the "Sub-Advisory Agreement" and together with the Advisory
Agreement, the "Agreements") among the Fund, the Advisor and Energy Income
Partners, LLC (the "Sub-Advisor") for a one-year period ending June 30, 2017 at
a meeting held on June 13, 2016. The Board determined that the continuation of
the Agreements is in the best interests of the Fund in light of the extent and
quality of the services provided and such other matters as the Board considered
to be relevant in the exercise of its reasonable business judgment.

To reach this determination, the Board considered its duties under the
Investment Company Act of 1940, as amended (the "1940 Act"), as well as under
the general principles of state law in reviewing and approving advisory
contracts; the requirements of the 1940 Act in such matters; the fiduciary duty
of investment advisors with respect to advisory agreements and compensation; the
standards used by courts in determining whether investment company boards have
fulfilled their duties; and the factors to be considered by the Board in voting
on such agreements. At meetings held on April 22, 2016 and June 13, 2016, the
Board, including the Independent Trustees, reviewed materials provided by the
Advisor and the Sub-Advisor responding to requests for information from counsel
to the Independent Trustees that, among other things, outlined the services
provided by the Advisor and the Sub-Advisor to the Fund (including the relevant
personnel responsible for these services and their experience); the advisory fee
rate payable by the Fund and the sub-advisory fees for the Fund as compared to
fees charged to a peer group of funds compiled by Management Practice, Inc.
("MPI"), an independent source (the "MPI Peer Group"), and as compared to fees
charged to other clients of the Advisor and the Sub-Advisor; expenses of the
Fund as compared to expense ratios of the funds in the MPI Peer Group;
performance information for the Fund; the nature of expenses incurred in
providing services to the Fund and the potential for economies of scale,


                                                                         Page 27





--------------------------------------------------------------------------------
ADDITIONAL INFORMATION (CONTINUED)
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                         NOVEMBER 30, 2016 (UNAUDITED)

if any; financial data on the Advisor and the Sub-Advisor; any fall out benefits
to the Advisor and its affiliate, First Trust Capital Partners, LLC ("FTCP"),
and the Sub-Advisor; and information on the Advisor's and the Sub-Advisor's
compliance programs. The Board reviewed initial materials with the Advisor at a
special meeting held on April 22, 2016, prior to which the Independent Trustees
and their counsel met separately to discuss the information provided by the
Advisor and the Sub-Advisor. Following the April meeting, independent legal
counsel on behalf of the Independent Trustees requested certain clarifications
and supplements to the materials provided, and the information provided in
response to those requests was considered at an executive session of the
Independent Trustees and independent legal counsel held prior to the June 13,
2016 meeting, as well as at the meeting held that day. The Board applied its
business judgment to determine whether the arrangements between the Fund and the
Advisor and among the Fund, the Advisor and the Sub-Advisor continue to be
reasonable business arrangements from the Fund's perspective as well as from the
perspective of shareholders. The Board determined that, given the totality of
the information provided with respect to the Agreements, the Board had received
sufficient information to renew the Agreements. The Board considered that
shareholders chose to invest or remain invested in the Fund knowing that the
Advisor and the Sub-Advisor manage the Fund.

In reviewing the Agreements, the Board considered the nature, extent and quality
of the services provided by the Advisor and the Sub-Advisor under the
Agreements. With respect to the Advisory Agreement, the Board considered that
the Advisor is responsible for the overall management and administration of the
Fund and reviewed all of the services provided by the Advisor to the Fund,
including the oversight of the Sub-Advisor, as well as the background and
experience of the persons responsible for such services. In reviewing the
services provided, the Board noted the compliance program that had been
developed by the Advisor and considered that it includes a robust program for
monitoring the Advisor's, the Sub-Advisor's and the Fund's compliance with the
1940 Act, as well as the Fund's compliance with its investment objective and
policies. In addition, as part of the Board's consideration of the Advisor's
services, the Advisor, in its written materials and at the April 22, 2016
meeting, described to the Board the scope of its ongoing investment in
additional infrastructure and personnel to maintain and improve the quality of
services provided to the Fund and the other funds in the First Trust Fund
Complex. With respect to the Sub-Advisory Agreement, the Board reviewed the
materials provided by the Sub-Advisor and considered the services that the
Sub-Advisor provides to the Fund, including the Sub-Advisor's day-to-day
management of the Fund's investments. In considering the Sub-Advisor's
management of the Fund, the Board noted the background and experience of the
Sub-Advisor's portfolio management team. In light of the information presented
and the considerations made, the Board concluded that the nature, extent and
quality of the services provided to the Fund by the Advisor and the Sub-Advisor
under the Agreements have been and are expected to remain satisfactory and that
the Sub-Advisor, under the oversight of the Advisor, has managed the Fund
consistent with its investment objective and policies.

The Board considered the advisory and sub-advisory fee rates payable under the
Agreements for the services provided. The Board noted that the sub-advisory fee
is paid by the Advisor from its advisory fee. The Board received and reviewed
information showing the advisory fee rates and expense ratios of the peer funds
in the MPI Peer Group, as well as advisory fee rates charged by the Advisor and
the Sub-Advisor to other fund and non-fund clients, as applicable. With respect
to the MPI Peer Group, the Board discussed with representatives of the Advisor
the limitations in creating a relevant peer group for the Fund, including that
(i) the Fund is unique in its composition, which makes assembling peers with
similar strategies and asset mix difficult; (ii) peer funds may use different
amounts and types of leverage with different costs associated with them or may
use no leverage; (iii) only two of the peer funds employ an advisor/sub-advisor
management structure and only one of those peer funds employs an unaffiliated
sub-advisor; and (iv) some of the peer funds are part of a larger fund complex
that may allow for additional economies of scale. The Board took these
limitations into account in considering the peer data, and noted that the
advisory fee rate payable by the Fund, based on average net assets, was above
the median of the MPI Peer Group. With respect to fees charged to other clients,
the Board considered differences between the Fund and other clients that limited
their comparability. In considering the advisory fee rate overall, the Board
also considered the Advisor's statement that it seeks to meet investor needs
through innovative and value-added investment solutions and the Advisor's
description of its long-term commitment to the Fund.

The Board considered performance information for the Fund. The Board noted the
process it has established for monitoring the Fund's performance and portfolio
risk on an ongoing basis, which includes quarterly performance reporting from
the Advisor and Sub-Advisor for the Fund. The Board determined that this process
continues to be effective for reviewing the Fund's performance. The Board
received and reviewed information comparing the Fund's performance for periods
ended December 31, 2015 to the performance of the MPI Peer Group and to a
blended benchmark index. In reviewing the Fund's performance as compared to the
performance of the MPI Peer Group, the Board took into account the limitations
described above with respect to creating a relevant peer group for the Fund.
Based on the information provided on net asset value performance, the Board
noted that the Fund outperformed the MPI Peer Group average for the one- and
three-year periods ended December 31, 2015. The Board also noted that the Fund
underperformed its blended benchmark index in the one- and three-year periods
ended December 31, 2015. In addition, the Board considered information provided
by the Advisor on the impact of leverage on the Fund's returns. The Board also
received information on the Fund's annual distribution rate as of December 31,
2015 and the Fund's average trading discount during 2015 and comparable
information for the peer group.

On the basis of all the information provided on the fees, expenses and
performance of the Fund and the ongoing oversight by the Board, the Board
concluded that the advisory and sub-advisory fees continue to be reasonable and
appropriate in light of the nature, extent and quality of the services provided
by the Advisor and the Sub-Advisor to the Fund under the Agreements.


Page 28





--------------------------------------------------------------------------------
ADDITIONAL INFORMATION (CONTINUED)
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                         NOVEMBER 30, 2016 (UNAUDITED)

The Board considered information and discussed with the Advisor whether there
were any economies of scale in connection with providing advisory services to
the Fund and noted the Advisor's statement that it expects its expenses to
increase over the next twelve months as the Advisor continues to make
investments in personnel and infrastructure. The Board determined that due to
the Fund's closed-end structure, the potential for realization of economies of
scale as Fund assets grow was not a material factor to be considered. The Board
considered the revenues and allocated costs (including the allocation
methodology) of the Advisor in serving as investment advisor to the Fund for the
twelve months ended December 31, 2015 and the estimated profitability level for
the Fund calculated by the Advisor based on such data, as well as complex-wide
and product-line profitability data for the same period. The Board noted the
inherent limitations in the profitability analysis, and concluded that, based on
the information provided, the Advisor's profitability level for the Fund was not
unreasonable. In addition, the Board considered fall-out benefits described by
the Advisor that may be realized from its relationship with the Fund. The Board
considered the ownership interest of FTCP in the Sub-Advisor and potential
fall-out benefits to the Advisor from such ownership interest. The Board noted
that in addition to the advisory fees paid by the Fund, the Advisor is
compensated for fund reporting services pursuant to a separate Fund Reporting
Services Agreement.

The Board considered that the Sub-Advisor's investment services expenses are
primarily fixed, and that the Sub-Advisor has made recent investments in
infrastructure and personnel. The Board considered that the sub advisory fee
rate was negotiated at arm's length between the Advisor and the Sub-Advisor. The
Board also considered information provided by the Sub-Advisor as to the
profitability of the Sub Advisory Agreement to the Sub-Advisor. The Board noted
the inherent limitations in the profitability analysis and concluded that the
profitability analysis for the Advisor was more relevant. The Board considered
fall-out benefits that may be realized by the Sub-Advisor from its relationship
with the Fund, including soft-dollar arrangements, and considered a summary of
such arrangements. The Board also considered the potential fall-out benefits to
the Sub-Advisor from FTCP's ownership interest in the Sub-Advisor.

Based on all of the information considered and the conclusions reached, the
Board, including the Independent Trustees, unanimously determined that the terms
of the Agreements continue to be fair and reasonable and that the continuation
of the Agreements is in the best interests of the Fund. No single factor was
determinative in the Board's analysis.


                                                                         Page 29





--------------------------------------------------------------------------------
BOARD OF TRUSTEES AND OFFICERS
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                         NOVEMBER 30, 2016 (UNAUDITED)



                                                                                                 NUMBER OF             OTHER
                                                                                               PORTFOLIOS IN      TRUSTEESHIPS OR
                                                                                              THE FIRST TRUST      DIRECTORSHIPS
       NAME, ADDRESS,           TERM OF OFFICE                                                 FUND COMPLEX       HELD BY TRUSTEE
      DATE OF BIRTH AND          AND LENGTH OF              PRINCIPAL OCCUPATIONS               OVERSEEN BY         DURING PAST
   POSITION WITH THE FUND         SERVICE (1)                DURING PAST 5 YEARS                  TRUSTEE             5 YEARS
------------------------------------------------------------------------------------------------------------------------------------
                                                        INDEPENDENT TRUSTEES
------------------------------------------------------------------------------------------------------------------------------------
                                                                                                   
Richard E. Erickson, Trustee   o Three-Year Term  Physician; President, Wheaton Orthopedics;        138        None
c/o First Trust Advisors L.P.                     Limited Partner, Gundersen Real Estate
120 E. Liberty Drive,          o Since Fund       Limited Partnership; Member, Sportsmed
  Suite 400                      Inception        LLC (April 2007 to November 2015)
Wheaton, IL 60187
D.O.B.: 04/51

Thomas R. Kadlec, Trustee      o Three-Year Term  President ADM Investor Services, Inc.             138        Director of ADM
c/o First Trust Advisors L.P.                     (Futures Commission Merchant)                                Investor Services,
120 E. Liberty Drive,          o Since Fund                                                                    Inc., ADM
  Suite 400                      Inception                                                                     Investor Services
Wheaton, IL 60187                                                                                              International, and
D.O.B.: 11/57                                                                                                  Futures Industry
                                                                                                               Association

Robert F. Keith, Trustee       o Three-Year Term  President, Hibs Enterprises (Financial and        138        Director of Trust
c/o First Trust Advisors L.P.                     Management Consulting)                                       Company of
120 E. Liberty Drive,          o Since Fund                                                                    Illinois
  Suite 400                      Inception
Wheaton, IL 60187
D.O.B.: 11/56

Niel B. Nielson, Trustee       o Three-Year Term  Managing Director and Chief Operating             138        Director of
c/o First Trust Advisors L.P.                     Officer (January 2015 to Present), Pelita                    Covenant
120 E. Liberty Drive,          o Since Fund       Harapan Educational Foundation (Educational                  Transport, Inc.
  Suite 400                      Inception        Products and Services); President and Chief                  (May 2003 -
Wheaton, IL 60187                                 Executive Officer (June 2012 to September                    May 2014)
D.O.B.: 03/54                                     2014), Servant Interactive LLC (Educational
                                                  Products and Services); President and Chief
                                                  Executive Officer (June 2012 to September
                                                  2014), Dew Learning LLC (Educational
                                                  Products and Services); President (June
                                                  2002 to June 2012), Covenant College

------------------------------------------------------------------------------------------------------------------------------------
                                                         INTERESTED TRUSTEE
------------------------------------------------------------------------------------------------------------------------------------
James A. Bowen(2), Trustee,    o Three-Year Term  Chief Executive Officer, First Trust              138        None
Chairman of the Board                             Advisors L.P. and First Trust Portfolios
120 E. Liberty Drive,          o Since Fund       L.P.; Chairman of the Board of Directors,
Wheaton, IL 60187                Inception        BondWave LLC Suite 400 (Software
D.O.B.: 09/55                                     Development Company) and Stonebridge
                                                  Advisors LLC (Investment Advisor)


-----------------------------

(1)   Currently, Robert F. Keith, as a Class I Trustee, is serving as a trustee
      until the Fund's 2017 annual meeting of shareholders. Richard E. Erickson
      and Thomas R. Kadlec, as Class II Trustees, are serving as trustees until
      the Fund's 2018 annual meeting of shareholders. James A. Bowen and Niel B.
      Nielson, as Class III Trustees, are serving as trustees until the Fund's
      2019 annual meeting of shareholders.

(2)   Mr. Bowen is deemed an "interested person" of the Fund due to his position
      as Chief Executive Officer of First Trust Advisors L.P., investment
      advisor of the Fund.


Page 30





--------------------------------------------------------------------------------
BOARD OF TRUSTEES AND OFFICERS (CONTINUED)
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                         NOVEMBER 30, 2016 (UNAUDITED)



    NAME, ADDRESS          POSITION AND OFFICES        TERM OF OFFICE AND                     PRINCIPAL OCCUPATIONS
  AND DATE OF BIRTH             WITH FUND              LENGTH OF SERVICE                       DURING PAST 5 YEARS
------------------------------------------------------------------------------------------------------------------------------------
                                                            OFFICERS(3)
------------------------------------------------------------------------------------------------------------------------------------
                                                                    
James M. Dykas         President and Chief           o Indefinite Term       Managing Director and Chief Financial Officer
120 E. Liberty Drive,  Executive Officer                                     (January 2016 to Present), Controller (January
  Suite 400                                          o Since January 2016    2011 to January 2016), Senior Vice President
Wheaton, IL 60187                                                            (April 2007 to January 2016), First Trust
D.O.B.: 01/66                                                                Advisors L.P. and First Trust Portfolios L.P.;
                                                                             Chief Financial Officer, BondWave LLC
                                                                             (Software Development Company) (January
                                                                             2016 to Present) and Stonebridge Advisors LLC
                                                                             (Investment Advisor) (January 2016 to Present)

Donald P. Swade        Treasurer, Chief              o Indefinite Term       Senior Vice President (July 2016 to Present),
120 E. Liberty Drive,  Financial Officer and                                 Vice President (April 2012 to July 2016), First
  Suite 400            Chief Accounting Officer      o Since January 2016    Trust Advisors L.P. and First Trust Portfolios
Wheaton, IL 60187                                                            L.P.; Vice President (September 2006 to April
D.O.B.: 08/72                                                                2012), Guggenheim Funds Investment Advisors, LLC/
                                                                             Claymore Securities, Inc.

W. Scott Jardine       Secretary and Chief           o Indefinite Term       General Counsel, First Trust Advisors L.P. and
120 E. Liberty Drive,  Legal Officer                                         First Trust Portfolios L.P.; Secretary and
  Suite 400                                          o Since Fund Inception  General Counsel, BondWave LLC; Secretary
Wheaton, IL 60187                                                            of Stonebridge Advisors LLC
D.O.B.: 05/60

Daniel J. Lindquist    Vice President                o Indefinite Term       Managing Director (July 2012 to Present),
120 E. Liberty Drive,                                                        Senior Vice President (September 2005 to July
  Suite 400                                          o Since Fund Inception  2012), First Trust Advisors L.P. and First Trust
Wheaton, IL 60187                                                            Portfolios L.P.
D.O.B: 02/70

Kristi A. Maher        Chief Compliance Officer      o Indefinite Term       Deputy General Counsel, First Trust Advisors
120 E. Liberty Drive,  and Assistant Secretary                               L.P. and First Trust Portfolios L.P.
  Suite 400                                          o Since Fund Inception
Wheaton, IL 60187
D.O.B.: 12/66


-----------------------------

(3)   Officers of the Fund have an indefinite term. The term "officer" means the
      president, vice president, secretary, treasurer, controller or any other
      officer who performs a policy making function.


                                                                         Page 31





--------------------------------------------------------------------------------
PRIVACY POLICY
--------------------------------------------------------------------------------

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                         NOVEMBER 30, 2016 (UNAUDITED)

PRIVACY POLICY

First Trust values our relationship with you and considers your privacy an
important priority in maintaining that relationship. We are committed to
protecting the security and confidentiality of your personal information.

SOURCES OF INFORMATION

We collect nonpublic personal information about you from the following sources:

      o     Information we receive from you and your broker-dealer, investment
            advisor or financial representative through interviews,
            applications, agreements or other forms;

      o     Information about your transactions with us, our affiliates or
            others;

      o     Information we receive from your inquiries by mail, e-mail or
            telephone; and

      o     Information we collect on our website through the use of "cookies".
            For example, we may identify the pages on our website that your
            browser requests or visits.

INFORMATION COLLECTED

The type of data we collect may include your name, address, social security
number, age, financial status, assets, income, tax information, retirement and
estate plan information, transaction history, account balance, payment history,
investment objectives, marital status, family relationships and other personal
information.

DISCLOSURE OF INFORMATION

We do not disclose any nonpublic personal information about our customers or
former customers to anyone, except as permitted by law. In addition to using
this information to verify your identity (as required under law), the permitted
uses may also include the disclosure of such information to unaffiliated
companies for the following reasons:

      o     In order to provide you with products and services and to effect
            transactions that you request or authorize, we may disclose your
            personal information as described above to unaffiliated financial
            service providers and other companies that perform administrative or
            other services on our behalf, such as transfer agents, custodians
            and trustees, or that assist us in the distribution of investor
            materials such as trustees, banks, financial representatives, proxy
            services, solicitors and printers.

      o     We may release information we have about you if you direct us to do
            so, if we are compelled by law to do so, or in other legally limited
            circumstances (for example to protect your account from fraud).

In addition, in order to alert you to our other financial products and services,
we may share your personal information within First Trust.

PRIVACY ONLINE

We allow third-party companies, including AddThis (a social media sharing
service), to collect certain anonymous information when you visit our website.
These companies may use non-personally identifiable information during your
visits to this and other websites in order to provide advertisements about goods
and services likely to be of greater interest to you. These companies typically
use a cookie, third party web beacon or pixel tags, to collect this information.
To learn more about this behavioral advertising practice, you can visit
www.networkadvertising.org.

CONFIDENTIALITY AND SECURITY

With regard to our internal security procedures, First Trust restricts access to
your nonpublic personal information to those First Trust employees who need to
know that information to provide products or services to you. We maintain
physical, electronic and procedural safeguards to protect your nonpublic
personal information.

POLICY UPDATES AND INQUIRIES

As required by federal law, we will notify you of our privacy policy annually.
We reserve the right to modify this policy at any time, however, if we do change
it, we will tell you promptly. For questions about our policy, or for additional
copies of this notice, please go to www.ftportfolios.com, or contact us at
1-800-621-1675 (First Trust Portfolios) or 1-800-222-6822 (First Trust
Advisors).


March 2016


Page 32





FIRST TRUST

INVESTMENT ADVISOR
First Trust Advisors L.P.
120 E. Liberty Drive, Suite 400
Wheaton, IL  60187

INVESTMENT SUB-ADVISOR
Energy Income Partners, LLC
10 Wright Street
Westport, CT 06880

ADMINISTRATOR,
FUND ACCOUNTANT &
TRANSFER AGENT
BNY Mellon Investment Servicing (US) Inc.
301 Bellevue Parkway
Wilmington, DE 19809

CUSTODIAN
The Bank of New York Mellon
101 Barclay Street, 20th Floor
New York, NY 10286

INDEPENDENT REGISTERED
PUBLIC ACCOUNTING FIRM
Deloitte & Touche LLP
111 S. Wacker Drive
Chicago, IL 60606

LEGAL COUNSEL
Chapman and Cutler LLP
111 W. Monroe Street
Chicago, IL 60603





[BLANK BACK COVER]





ITEM 2. CODE OF ETHICS.

(a)   The registrant, as of the end of the period covered by this report, has
      adopted a code of ethics that applies to the registrant's principal
      executive officer, principal financial officer, principal accounting
      officer or controller, or persons performing similar functions, regardless
      of whether these individuals are employed by the registrant or a third
      party.

(c)   There have been no amendments, during the period covered by this report,
      to a provision of the code of ethics that applies to the registrant's
      principal executive officer, principal financial officer, principal
      accounting officer or controller, or persons performing similar functions,
      regardless of whether these individuals are employed by the registrant or
      a third party, and that relates to any element of the code of ethics
      description.

(d)   The registrant has not granted any waivers, including an implicit waiver,
      from a provision of the code of ethics that applies to the registrant's
      principal executive officer, principal financial officer, principal
      accounting officer or controller, or persons performing similar functions,
      regardless of whether these individuals are employed by the registrant or
      a third party, that relates to one or more of the items set forth in
      paragraph (b) of this item's instructions.

ITEM 3. AUDIT COMMITTEE FINANCIAL EXPERT.

As of the end of the period covered by the report, the Registrant's board of
trustees has determined that Thomas R. Kadlec and Robert F. Keith are qualified
to serve as audit committee financial experts serving on its audit committee and
that each of them is "independent," as defined by Item 3 of Form N-CSR.

ITEM 4. PRINCIPAL ACCOUNTANT FEES AND SERVICES.

      (a) Audit Fees (Registrant) -- The aggregate fees billed for each of the
last two fiscal years for professional services rendered by the principal
accountant for the audit of the Registrant's annual financial statements or
services that are normally provided by the accountant in connection with
statutory and regulatory filings or engagements for those fiscal years were
$44,000 for the fiscal year ended November 30, 2015 and $44,000 for the fiscal
year ended November 30, 2016.

      (b) Audit-Related Fees (Registrant) -- The aggregate fees billed in each
of the last two fiscal years for assurance and related services by the principal
accountant that are reasonably related to the performance of the audit of the
registrant's financial statements and are not reported under paragraph (a) of
this Item were $0 for the fiscal year ended November 30, 2015 and $92 for the
fiscal year ended November 30, 2016.

      Audit-Related Fees (Investment Adviser) -- The aggregate fees billed in
each of the last two fiscal years for assurance and related services by the
principal accountant that are reasonably related to the performance of the audit
of the registrant's financial statements and are not reported under paragraph
(a) of this Item were $0 for the fiscal year ended November 30, 2015 and $0 for
the fiscal year ended November 30, 2016.

      (c) Tax Fees (Registrant) -- The aggregate fees billed in each of the last
two fiscal years for professional services rendered by the principal accountant
for tax compliance, tax advice, and tax planning to the registrant were $6,300
for the fiscal year ended November 30, 2015 and $6,300 for the fiscal year ended
November 30, 2016.

      Tax Fees (Investment Adviser) -- The aggregate fees billed in each of the
last two fiscal years for professional services rendered by the principal
accountant for tax compliance, tax advice, and tax planning to the registrant's
adviser were $0 for the fiscal year ended November 30, 2015 and $0 for the
fiscal year ended November 30, 2016.

      (d) All Other Fees (Registrant) -- The aggregate fees billed in each of
the last two fiscal years for products and services provided by the principal
accountant to the registrant, other than the services reported in paragraphs (a)
through (c) of this Item were $3,000 for the fiscal year ended November 30, 2015
and $0 for the fiscal year ended November 30, 2016.

      All Other Fees (Investment Adviser) -- The aggregate fees billed in each
of the last two fiscal years for products and services provided by the principal
accountant to the registrant's investment adviser, other than the services
reported in paragraphs (a) through (c) of this Item were $0 for the fiscal year
ended November 30, 2015 and $0 for the fiscal year ended November 30, 2016.

      (e)(1) Disclose the audit committee's pre-approval policies and procedures
described in paragraph (c)(7) of Rule 2-01 of Regulation S-X.

      Pursuant to its charter and its Audit and Non-Audit Services Pre-Approval
Policy, the Audit Committee (the "Committee") is responsible for the
pre-approval of all audit services and permitted non-audit services (including
the fees and terms thereof) to be performed for the Registrant by its
independent auditors. The Chairman of the Committee authorized to give such
pre-approvals on behalf of the Committee up to $25,000 and report any such
pre-approval to the full Committee.

      The Committee is also responsible for the pre-approval of the independent
auditor's engagements for non-audit services with the Registrant's adviser (not
including a sub-adviser whose role is primarily portfolio management and is
sub-contracted or overseen by another investment adviser) and any entity
controlling, controlled by or under common control with the investment adviser
that provides ongoing services to the Registrant, if the engagement relates
directly to the operations and financial reporting of the Registrant, subject to
the de minimis exceptions for non-audit services described in Rule 2-01 of
Regulation S-X. If the independent auditor has provided non-audit services to
the Registrant's adviser (other than any sub-adviser whose role is primarily
portfolio management and is sub-contracted with or overseen by another
investment adviser) and any entity controlling, controlled by or under common
control with the investment adviser that provides ongoing services to the
Registrant that were not pre-approved pursuant to the de minimis exception, the
Committee will consider whether the provision of such non-audit services is
compatible with the auditor's independence.

      (e)(2) The percentage of services described in each of paragraphs (b)
through (d) for the Registrant and the Registrant's investment adviser of this
Item that were approved by the audit committee pursuant to the pre-approval
exceptions included in paragraph (c)(7)(i)(c) or paragraph (c)(7)(ii) of Rule
2-01 of Regulation S-X are as follows:

                                     (b) 0%
                                     (c) 0%
                                     (d) 0%

      (f) The percentage of hours expended on the principal accountant's
engagement to audit the registrant's financial statements for the most recent
fiscal year that were attributed to work performed by persons other than the
principal accountant's full-time, permanent employees was less than fifty
percent.

      (g) The aggregate non-audit fees billed by the registrant's accountant for
services rendered to the Registrant, and rendered to the Registrant's investment
adviser (not including any sub-adviser whose role is primarily portfolio
management and is subcontracted with or overseen by another investment adviser),
and any entity controlling, controlled by, or under common control with the
adviser that provides ongoing services to the Registrant for the fiscal year
ended November 30, 2015 were $9,300 for the Registrant and $12,500 for the
Registrant's investment adviser, and for the fiscal year ended November 30, 2016
were $6,300 for the registrant and $13,000 for the Registrant's investment
adviser.

      (h) The Registrant's audit committee of its Board of Trustees has
determined that the provision of non-audit services that were rendered to the
Registrant's investment adviser (not including any sub-adviser whose role is
primarily portfolio management and is subcontracted with or overseen by another
investment adviser), and any entity controlling, controlled by, or under common
control with the investment adviser that provides ongoing services to the
Registrant that were not pre-approved pursuant to paragraph (c)(7)(ii) of Rule
2-01 of Regulation S-X is compatible with maintaining the principal accountant's
independence.

ITEM 5. AUDIT COMMITTEE OF LISTED REGISTRANTS.

The Registrant has a separately designated audit committee consisting of all the
independent trustees of the Registrant. The members of the audit committee are:
Thomas R. Kadlec, Niel B. Nielson, Richard E. Erickson and Robert F. Keith.

ITEM 6. INVESTMENTS.

(a)   Schedule of Investments in securities of unaffiliated issuers as of the
      close of the reporting period is included as part of the report to
      shareholders filed under Item 1 of this form.

(b)   Not applicable.

ITEM 7. DISCLOSURE OF PROXY VOTING POLICIES AND PROCEDURES FOR CLOSED-END
MANAGEMENT INVESTMENT COMPANIES.

                      PROXY VOTING POLICIES AND PROCEDURES

If an adviser exercises voting authority with respect to client securities,
Advisers Act Rule 206(4)-6 requires the adviser to adopt and implement written
policies and procedures reasonably designed to ensure that client securities are
voted in the best interest of the client. This is consistent with legal
interpretations which hold that an adviser's fiduciary duty includes handling
the voting of proxies on securities held in client accounts over which the
adviser exercises investment or voting discretion, in a manner consistent with
the best interest of the client.

Absent unusual circumstances, EIP exercises voting authority with respect to
securities held in client accounts pursuant to provisions in its advisory
agreements. Accordingly, EIP has adopted these policies and procedures with the
aim of meeting the following requirements of Rule 206(4)-6:

      o     ensuring that proxies are voted in the best interest of clients;

      o     addressing material conflicts that may arise between EIP's interests
            and those of its clients in the voting of proxies;

      o     disclosing to clients how they may obtain information on how EIP
            voted proxies with respect to the client's securities;

      o     describing to clients EIP's proxy voting policies and procedures
            and, upon request, furnishing a copy of the policies and procedures
            to the requesting client.


             ENGAGEMENT OF INSTITUTIONAL SHAREHOLDER SERVICES INC.

      With the aim of ensuring that proxies are voted in the best interest of
EIP clients, EIP has engaged Institutional Shareholder Services Inc. ("ISS"), as
its independent proxy voting service to provide EIP with proxy voting
recommendations, as well as to handle the administrative mechanics of proxy
voting. EIP has directed ISS to utilize its Proxy Voting Guidelines in making
recommendations to vote, as those guidelines may be amended from time to time.

                     CONFLICTS OF INTEREST IN PROXY VOTING

      There may be instances where EIP's interests conflict, or appear to
conflict, with client interests in the voting of proxies. For example, EIP may
provide services to, or have an investor who is a senior member of, a company
whose management is soliciting proxies. There may be a concern that EIP would
vote in favor of management because of its relationship with the company or a
senior officer. Or, for example, EIP (or its senior executive officers) may have
business or personal relationships with corporate directors or candidates for
directorship.

      EIP addresses these conflicts or appearances of conflicts by ensuring that
proxies are voted in accordance with the recommendations made by ISS, an
independent third party proxy voting service. As previously noted, in most
cases, proxies will be voted in accordance with ISS's own pre-existing proxy
voting guidelines.

                      DISCLOSURE ON HOW PROXIES WERE VOTED

      EIP will disclose to clients in Part 2A of its Form ADV how clients can
obtain information on how their proxies were voted, by contacting EIP at its
office in Westport, CT. EIP will also disclose in the ADV a summary of these
proxy voting policies and procedures and that upon request, clients will be
furnished a full copy of these policies and procedures.

      It is the responsibility of the CCO to ensure that any requests made by
clients for proxy voting information are responded to in a timely fashion and
that a record of requests and responses are maintained in EIP's books and
records.

                                PROXY MATERIALS

      EIP personnel will instruct custodians to forward to ISS all proxy
materials received on securities held in EIP client accounts.

                                  LIMITATIONS

      In certain circumstances, where EIP has determined that it is consistent
with the client's best interest, EIP will not take steps to ensure that proxies
are voted on securities in the client's account. The following are circumstances
where this may occur:

      *Limited Value: Proxies will not be required to be voted on securities in
a client's account if the value of the client's economic interest in the
securities is indeterminable or insignificant (less than $1,000). Proxies will
also not be required to be voted for any securities that are no longer held by
the client's account.

      *Securities Lending Program: When securities are out on loan, they are
transferred into the borrower's name and are voted by the borrower, in its
discretion. In most cases, EIP will not take steps to see that loaned securities
are voted. However, where EIP determines that a proxy vote, or other shareholder
action, is materially important to the client's account, EIP will make a good
faith effort to recall the security for purposes of voting, understanding that
in certain cases, the attempt to recall the security may not be effective in
time for voting deadlines to be met.

      *Unjustifiable Costs: In certain circumstances, after doing a cost-benefit
analysis, EIP may choose not to vote where the cost of voting a client's proxy
would exceed any anticipated benefits to the client of the proxy proposal.

                              OVERSIGHT OF POLICY

      The Chief Compliance Officer ("CCO") will follow the following procedures
with respect to the oversight of each proxy advisory firm retained by the
Adviser(s):

      o     Periodically, but no less frequently than semi-annually, sample
            proxy votes to review whether they complied with the Advisers' proxy
            voting policies and procedures including a review of those items
            that relate to certain proposals that may require more analysis
            (e.g. other than voting for directors).


      o     Collect information, no less frequently than annually, reasonably
            sufficient to support the conclusion that the proxy voting service
            provide has the capacity and competency to adequately analyze proxy
            issues. In this regard, the CCO shall consider, among other things:

      o     the adequacy and quality of the proxy advisory firm's staffing and
            personnel;

      o     the robustness of its policies and procedures regarding its ability
            to (i) ensure that its proxy voting recommendations are based on
            current and accurate information and (ii) identify and address any
            conflicts of interest; and

      o     any other considerations that the CCO believes would be appropriate
            in considering the nature and quality of the services provided by
            the proxy voting service.

      For purposes of these procedures, the CCO may rely upon information posted
by a proxy advisory firm on its website, provided that the proxy advisory firm
represents that the information is complete and current.

                            RECORDKEEPING ON PROXIES

      It is the responsibility of EIP's CCO to ensure that the following proxy
voting records are maintained:

      o     a copy of EIP's proxy voting policies and procedures;

      o     a copy of all proxy statements received on securities in client
            accounts (EIP may rely on ISS or the SEC's EDGAR system to satisfy
            this requirement);

      o     a record of each vote cast on behalf of a client (EIP relies on ISS
            to satisfy this requirement);

      o     a copy of any document prepared by EIP that was material to making a
            voting decision or that memorializes the basis for that decision;

      o     a copy of each written client request for information on how proxies
            were voted on the client's behalf or for a copy of EIP's proxy
            voting policies and procedures, and

      o     a copy of any written response to any client request for information
            on how proxies were voted on their behalf or furnishing a copy of
            EIP's proxy voting policies and procedures.

      The CCO will see that these books and records are made and maintained in
accordance with the requirements and time periods provided in Rule 204-2 of the
Advisers Act. For any registered investment companies advised by EIP, votes made
on its behalf will be stored electronically or otherwise recorded so that they
are available for preparation of the Form N-PX, Annual Report of Proxy Voting
Record of Registered Management Investment Company.

ITEM 8. PORTFOLIO MANAGERS OF CLOSED-END MANAGEMENT INVESTMENT COMPANIES.

(A)(1) IDENTIFICATION OF PORTFOLIO MANAGER(S) OR MANAGEMENT TEAM MEMBERS AND
       DESCRIPTION OF ROLE OF PORTFOLIO MANAGER(S) OR MANAGEMENT TEAM MEMBERS

Information provided as of February 1, 2017.

James Murchie, Chief Executive Officer and Founder of Energy Income Partners,
LLC ("EIP" or "Sub-Advisor"), and Eva Pao, principal of EIP, are co-portfolio
managers responsible for the day-to-day management of the registrant's
portfolio. Both portfolio managers have served in such capacity for 159 months.
John Tysseland is also a co-portfolio manager responsible for the day-to-day
management of the registrant's portfolio and has served in such capacity for 7
months.

JAMES J. MURCHIE
Co-Portfolio Manager

James J. Murchie is the Founder, Chief Executive Officer, co-portfolio manager
and a Principal of Energy Income Partners. After founding Energy Income Partners
in October 2003, Mr. Murchie and the Energy Income Partners investment team
joined Pequot Capital Management Inc. ("Pequot Capital") in December 2004. In
August 2006, Mr. Murchie and the Energy Income Partners investment team left
Pequot Capital and re-established Energy Income Partners. Prior to founding
Energy Income Partners, Mr. Murchie was a Portfolio Manager at Lawhill Capital
Partners, LLC ("Lawhill Capital"), a long/short equity hedge fund investing in
commodities and equities in the energy and basic industry sectors. Before
Lawhill Capital, Mr. Murchie was a Managing Director at Tiger Management, LLC,
where his primary responsibility was managing a portfolio of investments in
commodities and related equities. Mr. Murchie was also a Principal at Sanford C.
Bernstein. He began his career at British Petroleum, PLC. Mr. Murchie holds a BA
from Rice University and an MA from Harvard University.

EVA PAO
Co-Portfolio Manager

Eva Pao is a Principal of Energy Income Partners and is co-portfolio manager for
all its funds. She has been with EIP since inception in 2003. From 2005 to
mid-2006, Ms. Pao joined Pequot Capital Management during EIP's affiliation with
Pequot. Prior to Harvard Business School, Ms. Pao was a Manager at Enron Corp
where she managed a portfolio in Canadian oil and gas equities for Enron's
internal hedge fund that specialized in energy-related equities and managed a
natural gas trading book. Ms. Pao holds degrees from Rice University and Harvard
Business School.

JOHN K. TYSSELAND
Co-Portfolio Manager

John Tysseland is a Senior Research Analyst. From 2005 to 2014, he worked at
Citi Research most currently serving as a Managing Director where he covered
midstream energy companies and MLPs. From 1998 to 2005, he worked at Raymond
James & Associates as a Vice President who covered the oilfield service industry
and established the firm's initial coverage of MLPs in 2001. Prior to that, he
was an Equity Trader at Momentum Securities from 1997 to 1998 and an Assistant
Executive Director at Sumar Enterprises from 1996 to 1997. He graduated from The
University of Texas at Austin in 1996 with a BA in economics.

(A)(2) OTHER ACCOUNTS MANAGED BY PORTFOLIO MANAGER AND POTENTIAL CONFLICTS OF
       INTEREST

OTHER ACCOUNTS MANAGED BY PORTFOLIO MANAGER

Information provided as of November 30, 2016.



                                                                                                       # of Accounts    Total Assets
                                                                                                     Managed for which   for which
          Name of                                                         Total                       Advisory Fee is   Advisory Fee
    Portfolio Manager or                                              # of Accounts      Total           Based on       is Based on
        Team Member                        Type of Accounts*            Managed**        Assets         Performance     Performance
        -----------                        -----------------             -------        --------        -----------     -----------
                                                                                                         
1. James Murchie                   Registered Investment Companies:         7           $ 3631.9             0            $     0

                                   Other Pooled Investment Vehicles:        1           $  198.4             1            $ 198.4

                                   Other Accounts:                         698          $ 1379.2             1            $   2.3


2. EvaPao                          Registered Investment Companies:         7           $ 3631.9             0            $     0

                                   Other Pooled Investment Vehicles:        1           $  198.4             1            $ 198.4

                                   Other Accounts:                         698          $ 1379.2             1            $   2.3


3. John Tysseland                  Registered Investment Companies:         7           $ 3631.9             0            $     0

                                   Other Pooled Investment Vehicles:        1           $  198.4             1            $ 198.4

                                   Other Accounts:                         698          $ 1379.2             1            $   2.3



      *Examples for Types of Accounts:

      Other Registered Investment Companies: Any investment vehicle which is
      registered with the SEC, such as mutual funds of registered hedge funds.

      Other Pooled Investment Vehicles: Any unregistered account for which
      investor assets are pooled together, such as an unregistered hedge fund.

      Other Accounts: Any accounts managed not covered by the other two
      categories, such as privately managed accounts.

POTENTIAL CONFLICTS OF INTERESTS

      Energy Income Partners, LLC ("EIP" or the "Firm") investment professionals
who serve as portfolio managers to separately managed accounts, one of which
charges a performance fee, and provides its model portfolio to unified managed
accounts. The portfolio managers also serve as portfolio managers to one private
investment fund (the "Private Fund"), which charges a performance fee and a
registered mutual fund. EIP serves as a sub-advisor to three closed-end
management investment companies other than the Fund, an actively managed
exchange-traded fund (ETF), a sleeve of an ETF and a sleeve of a series of a
variable insurance trust.

      EIP has written policies and procedures regarding Order Aggregation and
Allocation to ensure that all accounts are treated fairly and equitably and that
no account is at a disadvantage. EIP will generally execute client transactions
on an aggregated basis when the Firm believes that to do so will allow it to
obtain best execution and to negotiate more favorable commission rates or avoid
certain transaction costs that might have otherwise been paid had such orders
been placed independently. EIP's ability to implement this may be limited by an
account's custodian, directed brokerage arrangements or other constraints
limiting EIP's use of a common executing broker.

      An aggregated order may be allocated on a basis different from that
specified herein provided that all clients receive fair and equitable treatment
and there is a legitimate reason for the different allocation. Reasons for
deviation may include (but are not limited to): a client's investment guidelines
and restrictions, available cash, liquidity or legal reasons, and to avoid
odd-lots or in cases when a normal allocation would result in a de minimis
allocation to one or more clients.

      Notwithstanding the above, due to differing tax ramifications and
compliance ratios, as well as dissimilar risk constraints and tolerances,
accounts with similar investment mandates may trade the same securities at
differing points in time. Additionally, for the reasons noted above, certain
accounts, including funds in which EIP, its affiliates and/or employees ("EIP
Funds") have a financial interest, may trade separately from other accounts and
participate in transactions which are deemed to be inappropriate for other
accounts with similar investment mandates. Further, during periods in which EIP
intends to trade the same securities across multiple accounts, transactions for
those accounts that must be traded through specific brokers and/or platforms
will often be executed after those for accounts over which EIP exercises full
brokerage discretion.

(A)(3) COMPENSATION STRUCTURE OF PORTFOLIO MANAGER(S) OR MANAGEMENT TEAM MEMBERS

Information provided as of November 30, 2016.

      The Fund's portfolio managers are compensated by a competitive minimum
base salary and share in the profits of EIP in relation to their ownership of
EIP. EIP's profits are influenced by the assets under management and the
performance of the Funds (i.e. all Funds managed or sub-advised by EIP) as
described above. Therefore, their success is based on the growth and success of
all EIP managed products, not just the funds that charge an incentive fee.

      The compensation of the EIP team members is determined according to
prevailing rates within the industry for similar positions.

(A)(4) DISCLOSURE OF SECURITIES OWNERSHIP

Information provided as of November 30, 2016.

                                   Dollar Range of Fund Shares
        Name                       Beneficially Owned
        -----                      ---------------------------
        James Murchie              $50,000-100,000
        Eva Pao                    $0
        John Tysseland             $50,000-100,000

(B)   Not applicable.


ITEM 9. PURCHASES OF EQUITY SECURITIES BY CLOSED-END MANAGEMENT INVESTMENT
COMPANY AND AFFILIATED PURCHASERS.

Not applicable.

ITEM 10. SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS.

There have been no material changes to the procedures by which the shareholders
may recommend nominees to the Registrant's board of trustees, where those
changes were implemented after the Registrant last provided disclosure in
response to the requirements of Item 407(c)(2)(iv) of Regulation S-K (17 CFR
229.407) (as required by Item 22(b)(15) of Schedule 14A (17 CFR 240.14a-101)),
or this Item.

ITEM 11. CONTROLS AND PROCEDURES.

(a)   The Registrant's principal executive and principal financial officers, or
      persons performing similar functions, have concluded that the Registrant's
      disclosure controls and procedures (as defined in Rule 30a-3(c) under the
      Investment Company Act of 1940, as amended (the "1940 Act") (17 CFR
      270.30a-3(c))) are effective, as of a date within 90 days of the filing
      date of the report that includes the disclosure required by this
      paragraph, based on their evaluation of these controls and procedures
      required by Rule 30a-3(b) under the 1940 Act (17 CFR 270.30a-3(b)) and
      Rules 13a-15(b) or 15d-15(b) under the Securities Exchange Act of 1934, as
      amended (17 CFR 240.13a-15(b) or 240.15d-15(b)).

(b)   There were no changes in the Registrant's internal control over financial
      reporting (as defined in Rule 30a-3(d) under the 1940 Act (17 CFR
      270.30a-3(d)) that occurred during the Registrant's second fiscal quarter
      of the period covered by this report that has materially affected, or is
      reasonably likely to materially affect, the Registrant's internal control
      over financial reporting.

ITEM 12. EXHIBITS.

(a)(1) Code of ethics, or any amendment thereto, that is the subject of
       disclosure required by Item 2 is attached hereto.

(a)(2) Certifications pursuant to Rule 30a-2(a) under the 1940 Act and Section
       302 of the Sarbanes-Oxley Act of 2002 are attached hereto.

(a)(3) Not applicable.

(b)    Certifications pursuant to Rule 30a-2(b) under the 1940 Act and Section
       906 of the Sarbanes- Oxley Act of 2002 are attached hereto.

(c)    Notices to the registrant's common shareholders in accordance with the
       order under Section 6(c) of the 1940 Act granting an exemption from
       Section 19(b) of the 1940 Act and Rule 19a-1 under the 1940 Act. (1)

      (1)   The Fund received exemptive relief from the Securities and Exchange
            Commission which permits the Fund to make periodic distributions of
            long-term capital gains as frequently as monthly each taxable year.
            The relief is conditioned, in part, on an undertaking by the Fund to
            make the disclosures to the holders of the Fund's common shares, in
            addition to the information required by Section 19(a) of the 1940
            Act and Rule 19a-1 thereunder. The Fund is likewise obligated to
            file with the SEC the information contained in any such notice to
            shareholders. In that regard, attached as an exhibit to this filing
            is a copy of such notice made during the period.





                                   SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, the registrant has duly caused this report to be
signed on its behalf by the undersigned, thereunto duly authorized.

(registrant)        First Trust Energy Infrastructure Fund
              ---------------------------------------------------

By (Signature and Title)*               /s/ James M. Dykas
                                        ----------------------------------------
                                        James M. Dykas, President and
                                        Chief Executive Officer
                                        (principal executive officer)

Date: January 24, 2017
     ------------------

Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, this report has been signed below by the
following persons on behalf of the registrant and in the capacities and on the
dates indicated.

By (Signature and Title)*               /s/ James M. Dykas
                                        ----------------------------------------
                                        James M. Dykas, President and
                                        Chief Executive Officer
                                        (principal executive officer)

Date: January 24, 2017
     ------------------

By (Signature and Title)*               /s/ Donald P. Swade
                                        ----------------------------------------
                                        Donald P. Swade, Treasurer,
                                        Chief Financial Officer and
                                        Chief Accounting Officer
                                        (principal financial officer)

Date: January 24, 2017
     ------------------

* Print the name and title of each signing officer under his or her signature.