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


                                    FORM 8-K

                                 CURRENT REPORT
     Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934

       Date of report (Date of earliest event reported) September 12, 2018



                     First Trust Energy Infrastructure Fund
             (Exact Name of Registrant as Specified in its Charter)



       Massachusetts                   811-22528                 45-2751056
(State or Other Jurisdiction    (Commission File Number)        (IRS Employer
     of Incorporation)                                       Identification No.)


   120 East Liberty Drive, Suite 400
           Wheaton, Illinois                                        60187
(Address of Principal Executive Offices)                          (Zip Code)


      Registrant's telephone number, including area code   (630) 765-8000


       ___________________________________________________________________
         (Former Name or Former Address, if Changed Since Last Report.)



Check the appropriate box below if the Form 8-K filing is intended to
simultaneously satisfy the filing obligation of the registrant under any of the
following provisions (see General Instruction A.2. below):

|_|   Written communications pursuant to Rule 425 under the Securities Act
      (17 CFR 230.425)

|_|   Soliciting material pursuant to Rule 14a-12 under the Exchange Act
      (17 CFR 240.14a-12)

|_|   Pre-commencement communications pursuant to Rule 14d-2(b) under the
      Exchange Act (17 CFR 240.14d-2(b))

|_|   Pre-commencement communications pursuant to Rule 13e-4(c) under the
      Exchange Act (17 CFR 240.13e-4(c))





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Item 7.01 Regulation FD Disclosure.

First Trust Energy Infrastructure Fund (the "Fund") is filing herewith a press
release issued on September 12, 2018, as Exhibit 99.1. The press release was
issued by First Trust Advisors L.P. to report that on September 14, 2018, Energy
Income Partners, LLC, investment sub-advisor for the Fund, will release an
update on the market and the Fund. Details regarding the update are contained in
the press release included herein.

Item 9.01    Financial Statements and Exhibits.


(d) Exhibits

        Exhibit
        Number        Description

           99.1       Press release of First Trust Advisors L.P. dated
                      September 12, 2018.





                                   SIGNATURES

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

Dated: September 12, 2018        FIRST TRUST ENERGY INFRASTRUCTURE FUND

                                 By: /s/ W. Scott Jardine

                                        ----------------------------------
                                 Name:   W. Scott Jardine
                                 Title:  Secretary





                                 EXHIBIT INDEX

        Exhibit
        Number        Description

           99.1       Press release of First Trust Advisors L.P. dated
                      September 12, 2018.