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

                                    FORM N-Q

       QUARTERLY SCHEDULE OF PORTFOLIO HOLDINGS OF REGISTERED MANAGEMENT
                               INVESTMENT COMPANY

                  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: February 28, 2017
                                           -------------------

Form N-Q is to be used by management investment companies, other than small
business investment companies registered on Form N-5 (ss.ss. 239.24 and 274.5 of
this chapter), to file reports with the Commission, not later than 60 days after
the close of the first and third fiscal quarters, pursuant to rule 30b1-5 under
the Investment Company Act of 1940 (17 CFR 270.30b1-5). The Commission may use
the information provided on Form N-Q in its regulatory, disclosure review,
inspection, and policymaking roles.

A registrant is required to disclose the information specified by Form N-Q, and
the Commission will make this information public. A registrant is not required
to respond to the collection of information contained in Form N-Q 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 the
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. SCHEDULE OF INVESTMENTS. The Schedule(s) of Investments is attached
herewith.


FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS
FEBRUARY 28, 2017 (UNAUDITED)




    SHARES                                   DESCRIPTION                                   VALUE
---------------  --------------------------------------------------------------------  --------------
COMMON STOCKS - 86.7%
                                                                                 
                 ELECTRIC UTILITIES - 19.1%
         14,500  American Electric Power Co., Inc. (a)...............................  $      971,065
        114,500  Duke Energy Corp. ..................................................       9,451,975
         15,900  Edison International ...............................................       1,267,866
        197,900  Emera, Inc. (CAD) (a)...............................................       6,786,888
        180,000  Eversource Energy (a)...............................................      10,558,800
        167,200  Exelon Corp. (a)....................................................       6,137,912
        165,400  Fortis, Inc. (CAD) (a)..............................................       5,246,425
        265,300  Hydro One Ltd. (CAD) (a) (b)........................................       4,713,959
         64,000  IDACORP, Inc. (a)...................................................       5,307,520
         32,100  NextEra Energy, Inc. (a)............................................       4,205,100
        112,300  Southern (The) Co. (a)..............................................       5,707,086
        153,400  Xcel Energy, Inc. (a)...............................................       6,705,114
                                                                                       --------------
                                                                                           67,059,710
                                                                                       --------------

                 GAS UTILITIES - 5.7%
         45,600  Atmos Energy Corp. (a)..............................................       3,570,024
         60,310  Chesapeake Utilities Corp. (a)......................................       4,158,375
        126,000  New Jersey Resources Corp. (a)......................................       4,964,400
        150,018  UGI Corp. ..........................................................       7,235,368
                                                                                       --------------
                                                                                           19,928,167
                                                                                       --------------

                 MULTI-UTILITIES - 21.0%
         90,900  Alliant Energy Corp. (a)............................................       3,588,732
        162,200  ATCO, Ltd., Class I (CAD) (a).......................................       5,541,813
        211,700  Canadian Utilities Ltd., Class A (CAD) (a)..........................       5,696,550
        163,800  CMS Energy Corp. (a)................................................       7,292,376
        179,500  National Grid PLC, ADR (a)..........................................      10,922,575
        179,800  NiSource, Inc. (a)..................................................       4,299,018
        257,000  Public Service Enterprise Group, Inc. (a)...........................      11,816,860
        102,900  SCANA Corp. (a).....................................................       7,136,115
         92,900  Sempra Energy (a)...................................................      10,245,941
        120,200  WEC Energy Group, Inc. (a)..........................................       7,244,454
                                                                                       --------------
                                                                                           73,784,434
                                                                                       --------------

                 OIL, GAS & CONSUMABLE FUELS - 40.6%
      1,927,487  Enbridge Energy Management, LLC (a) (c).............................      33,538,275
        595,200  Enbridge Income Fund Holdings, Inc. (CAD) (a).......................      15,303,479
        136,400  Enbridge, Inc. .....................................................       5,708,340
        325,700  Inter Pipeline, Ltd. (CAD) (a)......................................       6,829,352
        172,100  Keyera Corp. (CAD) (a)..............................................       5,067,634
        576,175  Kinder Morgan, Inc. (a).............................................      12,278,289
         74,900  ONEOK, Inc. ........................................................       4,048,345
        637,100  Plains GP Holdings L.P. ............................................      20,941,477
        115,600  Targa Resources Corp. (a)...........................................       6,531,400
        423,170  TransCanada Corp. (a)...............................................      19,461,588
        456,600  Williams (The) Cos., Inc. ..........................................      12,940,044
                                                                                       --------------
                                                                                          142,648,223
                                                                                       --------------


                     See Notes to Portfolio of Investments





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
FEBRUARY 28, 2017 (UNAUDITED)




    SHARES/
     UNITS                                   DESCRIPTION                                   VALUE
---------------  --------------------------------------------------------------------  --------------
COMMON STOCKS (CONTINUED)
                                                                                 
                 WATER UTILITIES - 0.3%
         15,900  American Water Works Co., Inc. (a)..................................  $    1,240,200
                                                                                       --------------
                 TOTAL COMMON STOCKS ................................................     304,660,734
                 (Cost $295,268,953)                                                   --------------

MASTER LIMITED PARTNERSHIPS - 36.7%

                 CHEMICALS - 0.1%
         22,000  Westlake Chemical Partners, L.P. (a)................................         553,300
                                                                                       --------------

                 GAS UTILITIES - 2.1%
        122,152  AmeriGas Partners, L.P. (a).........................................       5,737,479
         62,500  Suburban Propane Partners, L.P. (a).................................       1,634,375
                                                                                       --------------
                                                                                            7,371,854
                                                                                       --------------

                 INDEPENDENT POWER AND RENEWABLE ELECTRICITY PRODUCERS - 4.1%
        465,555  NextEra Energy Partners, L.P. (a) (d)...............................      14,329,783
                                                                                       --------------

                 OIL, GAS & CONSUMABLE FUELS - 30.4%
         79,700  Alliance Holdings GP, L.P. (a)......................................       2,279,420
        339,930  Alliance Resource Partners, L.P. (a)................................       7,767,400
         65,700  Buckeye Partners, L.P. (a)..........................................       4,528,044
         44,600  Dominion Midstream Partners, L.P. ..................................       1,380,370
        727,700  Enterprise Products Partners, L.P. (a)..............................      20,397,431
        112,200  EQT Midstream Partners, L.P. (a)....................................       8,843,604
        226,976  Holly Energy Partners, L.P. (a).....................................       8,152,978
         85,300  Magellan Midstream Partners, L.P. (a)...............................       6,611,603
        123,972  NGL Energy Partners, L.P. (a).......................................       2,752,178
        109,800  ONEOK Partners, L.P. (a)............................................       5,751,324
        103,600  Phillips 66 Partners, L.P. (a)......................................       5,763,268
         65,000  Plains All American Pipeline, L.P. .................................       2,085,200
         41,000  Shell Midstream Partners, L.P. .....................................       1,343,160
        265,300  Spectra Energy Partners, L.P. (a)...................................      11,866,869
         47,328  Tallgrass Energy Partners, L.P. (a).................................       2,530,155
        151,495  TC PipeLines, L.P. (a)..............................................       9,250,285
         56,002  TransMontaigne Partners, L.P. (a)...................................       2,479,209
         75,000  Williams Partners, L.P. ............................................       3,022,500
                                                                                       --------------
                                                                                          106,804,998
                                                                                       --------------
                 TOTAL MASTER LIMITED PARTNERSHIPS ..................................     129,059,935
                 (Cost $103,838,871)                                                   --------------

REAL ESTATE INVESTMENT TRUSTS - 1.2%

                 EQUITY REAL ESTATE INVESTMENT TRUSTS - 1.2%
        142,050  InfraREIT, Inc. (a).................................................       2,365,132
         49,101  CorEnergy Infrastructure Trust, Inc. ...............................       1,752,415
                                                                                       --------------
                 TOTAL REAL ESTATE INVESTMENT TRUSTS ................................       4,117,547
                 (Cost $4,598,708)                                                     --------------

                 TOTAL INVESTMENTS - 124.6% .........................................     437,838,216
                 (Cost $403,706,532) (e)                                               --------------



                     See Notes to Portfolio of Investments





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
FEBRUARY 28, 2017 (UNAUDITED)




   NUMBER OF
   CONTRACTS                                 DESCRIPTION                                   VALUE
---------------  --------------------------------------------------------------------  --------------
CALL OPTIONS WRITTEN - (0.5%)
                                                                                 
                 CMS Energy Corp. Call
          1,100  @ $45.00 due March 2017.............................................  $      (44,000)
                                                                                       --------------
                 Enbridge, Inc. Calls
            200  @  45.00 due March 2017 (f).........................................          (1,000)
            800  @  45.00 due April 2017.............................................         (20,000)
            200  @  47.50 due July 2017..............................................          (9,000)
                                                                                       --------------
                                                                                              (30,000)
                                                                                       --------------
                 Eversource Energy Call
            400  @  60.00 due April 2017.............................................         (28,400)
                                                                                       --------------
                 Exelon Corp. Call
          1,500  @  37.00 due April 2017.............................................        (142,500)
                                                                                       --------------
                 Kinder Morgan, Inc. Calls
          1,200  @  23.00 due March 2017.............................................          (6,000)
            100  @  24.00 due March 2017.............................................            (200)
          3,300  @  23.00 due April 2017.............................................         (72,600)
            500  @  24.00 due June 2017..............................................         (12,000)
                                                                                       --------------
                                                                                              (90,800)
                                                                                       --------------
                 National Grid PLC Call
          1,400  @  60.00 due March 2017.............................................        (126,000)
                                                                                       --------------
                 NextEra Energy, Inc. Calls
            100  @  130.00 due March 2017............................................         (22,500)
            100  @  135.00 due April 2017............................................         (11,500)
                                                                                       --------------
                                                                                              (34,000)
                                                                                       --------------
                 NiSource, Inc. Call
          1,600  @  23.00 due April 2017.............................................        (184,000)
                                                                                       --------------
                 ONEOK, Inc. Calls
            100  @  57.50 due April 2017.............................................         (12,000)
            600  @  60.00 due April 2017.............................................         (27,000)
                                                                                       --------------
                                                                                              (39,000)
                                                                                       --------------
                 Plains All American Pipeline L.P. Call
            500  @  33.00 due April 2017.............................................         (35,000)
                                                                                       --------------
                 Public Service Enterprise Group, Inc. Call
          2,300  @  45.00 due March 2017.............................................        (273,700)
                                                                                       --------------
                 Sempra Energy Call
            600  @  110.00 due April 2017............................................        (160,800)
                                                                                       --------------
                 Southern (The) Co. Call
          1,100  @  52.50 due April 2017.............................................         (46,200)
                                                                                       --------------


                     See Notes to Portfolio of Investments





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
FEBRUARY 28, 2017 (UNAUDITED)




   NUMBER OF
   CONTRACTS                                 DESCRIPTION                                   VALUE
---------------  --------------------------------------------------------------------  --------------
CALL OPTIONS WRITTEN (CONTINUED)
                                                                                
                 Targa Resources Corp. Calls
          1,000  @ $60.00 due April 2017.............................................  $     (115,000)
            100  @  60.00 due July 2017..............................................         (26,500)
                                                                                       --------------
                                                                                             (141,500)
                                                                                       --------------
                 TransCanada Corp. Calls
          2,900  @  50.00 due March 2017.............................................          (5,800)
            800  @  50.00 due May 2017...............................................         (20,000)
            100  @  50.00 due August 2017............................................          (5,900)
                                                                                       --------------
                                                                                              (31,700)
                                                                                       --------------
                 UGI Corp. Call
          1,200  @  50.00 due April 2017.............................................         (36,000)
                                                                                       --------------
                 WEC Energy Group, Inc. Call
            900  @  60.00 due March 2017.............................................         (76,500)
                                                                                       --------------
                 Williams (The) Cos., Inc. Calls
            200  @  30.00 due March 2017.............................................          (3,000)
          2,700  @  31.00 due April 2017.............................................         (81,000)
          1,600  @  35.00 due May 2017...............................................         (20,000)
                                                                                       --------------
                                                                                             (104,000)
                                                                                       --------------
                 TOTAL CALL OPTIONS WRITTEN .........................................      (1,624,100)
                 (Premiums received $1,823,689)                                        --------------

                 OUTSTANDING LOAN - (35.4%) .........................................    (124,500,000)

                 NET OTHER ASSETS AND LIABILITIES - 11.3% ...........................      39,569,685
                                                                                       --------------
                 NET ASSETS - 100.0% ................................................ $   351,283,801
                                                                                       ==============


-------------------------------------------
(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 beinregistered 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 which pays in-kind ("PIK") distributions.
      For fiscal year-to-date period (December 1, 2016 through February 28,
      2017), the fund received 48,808 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 financial reporting purposes, which approximates the
      aggregate cost for federal income tax purposes. As of February 28, 2017,
      the aggregate gross unrealized appreciation for all securities in which
      there was an excess of value over tax cost was $43,062,145 and the
      aggregate gross unrealized depreciation for all securities in which there
      was an excess of tax cost over value was $8,930,461.

(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 February 28, 2017, securities noted as such
      are valued at $(1,000) or (0.0)% of net assets.


                     See Notes to Portfolio of Investments





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
FEBRUARY 28, 2017 (UNAUDITED)


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:


                         FLOATING      EXPIRATION    NOTIONAL     FIXED
    COUNTERPARTY         RATE (1)         DATE        AMOUNT     RATE (1)       VALUE
-----------------------------------------------------------------------------------------
                                                             
Bank of Nova Scotia    1 month LIBOR    10/08/20   $ 36,475,000   2.121%    $   (652 686)
Bank of Nova Scotia    1 month LIBOR    09/03/24     36,475,000   2.367%        (898,565)
                                                   ------------             -------------
                                                   $ 72,950,000             $ (1,551,251)
                                                   ============             =============



(1)   The Fund pays the fixed rate and receives the floating rate. The floating
      rate on February 28, 2017 was 0.775% and 0.780%, respectively.

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

VALUATION INPUTS

A summary of the inputs used to value the Fund's investments as of February 28,
2017 is as follows (see Note 2A - Portfolio Valuation in the Notes to Portfolio
of Investments):


                                                    ASSETS TABLE
                                                                                        LEVEL 2           LEVEL 3
                                                     TOTAL            LEVEL 1         SIGNIFICANT       SIGNIFICANT
                                                   VALUE AT           QUOTED          OBSERVABLE       UNOBSERVABLE
                                                   2/28/2017          PRICES            INPUTS            INPUTS
                                                ---------------   ---------------   ---------------   ---------------
                                                                                          
Common Stocks*................................  $   304,660,734   $   304,660,734   $            --   $            --
Master Limited Partnerships*..................      129,059,935       129,059,935                --                --
Real Estate Investment Trusts*................        4,117,547         4,117,547                --                --
                                                ---------------   ---------------   ---------------   ---------------
Total Investments.............................  $   437,838,216   $   437,838,216   $            --   $            --
                                                ===============   ===============   ===============   ===============

                                                  LIABILITIES TABLE
                                                                                        LEVEL 2           LEVEL 3
                                                     TOTAL            LEVEL 1         SIGNIFICANT       SIGNIFICANT
                                                   VALUE AT           QUOTED          OBSERVABLE       UNOBSERVABLE
                                                   2/28/2017          PRICES            INPUTS            INPUTS
                                                ---------------   ---------------   ---------------   ---------------
Call Options Written..........................  $   (1,624,100)   $    (1,574,100)  $       (50,000)  $            --
Interest Rate Swaps**.........................      (1,551,251)                --        (1,551,251)               --
                                                ---------------   ---------------   ---------------   ---------------
                                                $   (3,175,351)   $    (1,574,100)  $    (1,601,251)  $
                                                ==============    ===============   ===============   ===============



*   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 February 28, 2017.


                     See Notes to Portfolio of Investments





NOTES TO PORTFOLIO OF INVESTMENTS

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                         FEBRUARY 28, 2017 (UNAUDITED)


                                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 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."

                       2. SIGNIFICANT ACCOUNTING POLICIES

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, master limited partnerships ("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.

      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;





NOTES TO PORTFOLIO OF INVESTMENTS (CONTINUED)

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                         FEBRUARY 28, 2017 (UNAUDITED)


      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 February 28, 2017, is
included with the Fund's Portfolio of Investments.

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. 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. 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.





NOTES TO PORTFOLIO OF INVESTMENTS (CONTINUED)

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                         FEBRUARY 28, 2017 (UNAUDITED)


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. 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 February 28, 2017 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.

The Fund held interest rate swap agreements at February 28, 2017 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.

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.

E. 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.





NOTES TO PORTFOLIO OF INVESTMENTS (CONTINUED)

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                         FEBRUARY 28, 2017 (UNAUDITED)


                           3. DERIVATIVE TRANSACTIONS

Written option activity for the Fund was as follows:

                                                       NUMBER OF
WRITTEN OPTIONS                                        CONTRACTS      PREMIUMS
--------------------------------------------------------------------------------
Options outstanding at November 30, 2016.............     23,800    $ 1,367,185
Options Written......................................     32,800      2,001,808
Options Expired......................................    (21,000)    (1,150,321)
Options Exercised....................................     (6,300)      (391,987)
Options Closed.......................................       (100)        (2,996)
                                                       ---------    -----------
Options outstanding at February 28, 2017.............     29,200    $ 1,823,689
                                                       =========    ===========

The average volume of interest rate swaps was $72,950,000 for the fiscal
year-to-date period (December 1, 2016 through February 28, 2017).





ITEM 2. 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 last fiscal quarter
       that have materially affected, or are reasonably likely to materially
       affect, the registrant's internal control over financial reporting.

ITEM 3. EXHIBITS.

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


                                   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:  April 11, 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:  April 11, 2017
     ------------------

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

Date:  April 11, 2017
     ------------------


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