Center Coast Brookfield MLP & Energy Infrastructure Fund

Filed Pursuant to Rule 497(e)

Registration File No.: 333-229567

CENTER COAST BROOKFIELD MLP & ENERGY INFRASTRUCTURE FUND

Supplement dated June 8, 2020

to the

Prospectus Supplement dated April 22, 2020

to the Prospectus dated January 21, 2020

This is a supplement (the “Supplement”), to the Prospectus Supplement, dated April 22, 2020, to the Prospectus, dated January 21, 2020, of Center Coast Brookfield MLP & Energy Infrastructure Fund (the “Fund”) relating to the issuance and sale of Common Shares pursuant a second amended and restated distribution agreement, dated January 21, 2020 (the “Distribution Agreement”), between the Fund and Foreside Fund Services, LLC (“Foreside” or the “Distributor”), pursuant to which the Fund may offer and sell up to 20,679,822 Common Shares, from time to time, through the Distributor, as agent for the Fund, in transactions that are deemed to be “at the market” as defined in Rule 415 under the Securities Act of 1933, as amended.

You should read this Supplement in conjunction with the Prospectus Supplement, dated April 22, 2020, and the Prospectus, dated January 21, 2020. A Statement of Additional Information, dated January 21, 2020, containing additional information about the Fund, has been filed with the SEC and is incorporated by reference in its entirety into the Prospectus. Certain capitalized terms used and not defined herein have the meanings set forth in the Prospectus Supplement or Prospectus.

RECENT DEVELOPMENTS

Market and Net Asset Value Information

As of June 4, 2020, the last reported sales price on the NYSE, the NAV per Common Share and the percentage discount to NAV were $1.32, $1.36 and 2.94%, respectively. As of June 4, 2020, 49,299,453 Common Shares were outstanding.

The Fund cannot predict whether its Common Shares will trade in the future at a premium to or discount from NAV, or the level of any premium or discount. Shares of closed-end investment companies frequently trade at a discount from NAV. As a result of recent market condition, the Fund’s NAV may fluctuate significantly.

Distributions

The Fund plans to make distributions to Common Shareholders on a quarterly basis. On June 5, 2020, the Board of Trustees declared the Fund’s quarterly distribution for June 2020 as follows:


	Record Date	Ex Date	Payable Date	Amount Per Share
June 2020	June 17, 2020	June 16, 2020	June 25, 2020	$0.0225

Declaration and payment of future distributions is subject to approval by the Fund’s Board of Trustees. Future distributions will be made if and when declared by the Fund’s Board of Trustees, based on a consideration of a number of factors, including the Fund’s continued compliance with the asset coverage requirements of the Investment Company Act of 1940, as amended, and the terms and financial covenants of its senior securities, the distributions received from the Fund’s portfolio investments, the Fund’s deferred income tax liability/asset balance, the Fund’s financial performance and the Fund’s available cash. There can be no assurance that the amount or timing of distributions in the future will be equal or similar to past distributions or that the Board of Trustees will not decide to suspend or discontinue the payment of distributions in the future. Distributions may be paid from sources other than ordinary income, such as short-term capital gain, long-term capital gain or return of capital.

Reverse Share Split

On June 5, 2020, the Fund announced that its Board of Trustees approved a 10-for-1 reverse share split, effective after the market close on July 2, 2020. As a result of the reverse share split, every ten (10) of the Fund’s outstanding Common Shares will be converted into one (1) Common Share. A reverse share split will decrease the Fund’s Common Shares outstanding and potentially increase the market price per Common Share by a proportional amount.