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                     FIRST TRUST ENERGY INFRASTRUCTURE FUND
                       120 EAST LIBERTY DRIVE, SUITE 400
                            WHEATON, ILLINOIS 60187


February 2, 2016

Dear Shareholders:

I am pleased to announce that the Board of Trustees of First Trust Energy
Infrastructure Fund (NYSE: FIF) (the "Fund") has recently approved a change to
the Fund's investment strategy as described in the table below. The Fund is a
non-diversified, closed-end management investment company which commenced
investment operations in September 2011. 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. The
Fund's investment objective is not changing. The Fund's investment strategy that
is changing is non-fundamental and is not required to be approved by
shareholders. The Fund anticipates implementing the change to the investment
strategy beginning on or around April 11, 2016.


Current Investment Strategy                  New Investment Strategy

To generate additional income, the           To generate additional income, the
Fund  may write (or sell) covered            Fund may write (or sell) covered
call options on up to 30% of its             call options on up to 35% of its
Managed Assets.                              Managed Assets.


Managed Assets means the average daily gross asset value of the Fund (which
includes assets attributable to the Fund's Preferred Shares, if any, and the
principal amount of any borrowings), minus the sum of the Fund's accrued and
unpaid dividends on any outstanding Preferred Shares and accrued liabilities
(other than the principal amount of any borrowings of money incurred or of
commercial paper or notes issued by the Fund). The Fund's covered call risk may
increase as a result of its new investment strategy. Writing covered call
options may cause the Fund to forgo the opportunity to profit from part of the
increase in the market prices of the securities in its portfolio.

First Trust Advisors L.P., the Fund's investment advisor, along with its
affiliate, First Trust Portfolios L.P., are privately-held companies which
provide a variety of investment services, including asset management and
financial advisory services, with collective assets under management or
supervision of approximately $104 billion as of December 31, 2015, through unit
investment trusts, exchange-traded funds, closed-end funds, mutual funds and
separate managed accounts.

Energy Income Partners, LLC ("EIP") serves as the Fund's investment sub-advisor
and provides advisory services to a number of investment companies and
partnerships for the purpose of investing in MLPs and other energy
infrastructure securities. EIP is one of the early investment advisors
specializing in this area. As of December 31, 2015, EIP managed or supervised
approximately $4.2 billion in client assets.

The Fund's daily closing New York Stock Exchange price and net asset value per
share as well as other information, including information relating to the Fund's
investment objective and policies, risk considerations and expenses, can be
found at www.ftportfolios.com or by calling 1-800-988-5891.

Sincerely,

/s/ James A. Bowen

James A. Bowen
Chairman of the Board of Trustees of First Trust Energy Infrastructure Fun