CENTER COAST MLP & INFRASTRUCTURE FUND

Supplement dated September 23, 2016

to the Prospectus Supplement dated May 27, 2016

to the Prospectus dated May 6, 2016

This is a supplement (the “Supplement”), to the Prospectus Supplement dated May 27, 2016 (as further supplemented from time to time, the “Prospectus Supplement”) to the Prospectus dated May 6, 2016 of Center Coast MLP & Infrastructure Fund (the “Fund”) relating to the issuance and sale of Common Shares pursuant a distribution agreement, dated May 27, 2016 (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 4,000,000 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.

This Supplement updates certain information in the Prospectus Supplement, and the related Prospectus as follows. Certain capitalized terms used and not defined herein have the meanings set forth in the Prospectus Supplement or the Prospectus.

Recent Developments — Issuance of Mandatory Redeemable Preferred Shares

On September 22, 2016, the Fund completed a private placement of 2,000 shares of Series A Mandatory Redeemable Preferred Shares (“MRP Shares”). Each MRP Share has a liquidation preference of $25,000, resulting in an aggregate liquidation preference of $50 million for all MRP Shares. The MRP Shares will pay quarterly cash dividends at a rate of 4.29% per annum. The MRP Shares have a term redemption date of September 26, 2026.

The MRP Shares have been assigned a rating of “A” by Fitch Ratings, Inc. If the ratings of the MRP Shares are downgraded, the Fund’s dividend expense may increase.

Net proceeds from the offering of the MRP Shares will be used to invest in additional MLP and energy infrastructure assets, refinance existing Financial Leverage and for general corporate purposes.

As of September 16, 2016, the Fund had outstanding Borrowings under the Credit Agreement of $84.6 million (representing approximately 27.8% of the Fund’s Managed Assets).  After giving effect to the issuance of the MRP Shares, but before any refinancing of the Fund’s Borrowings using the proceeds of the issuance of the MRP Shares, the Fund had total Financial Leverage of representing 38% of the Fund’s Managed Assets.

Any Borrowings and Preferred Stock have seniority over the Common Stock. The costs associated with the issuance and use of Financial Leverage will be borne by the holders of the Common Shares. Financial Leverage is a speculative technique and investors should note that there are special risks and costs associated with Financial Leverage. There is no assurance that the Fund’s Financial Leverage strategy will be successful.

If the Fund is unable to refinance MRP Shares upon the term redemption date, the Fund may be forced to sell portfolio securities to redeem MRP Shares. If the Fund is required to sell portfolio securities to redeem MRP Shares at the term redemption date or to maintain asset coverage ratios, such sales may be at prices lower than what the Fund would otherwise realize if the Fund was not required to sell such securities at such time. Additionally, the Fund may be unable to refinance MRP Shares or sell a sufficient amount of portfolio securities to redeem MRP Shares at the term redemption date or to maintain asset

coverage ratios, which could cause an event of default on the MRP Shares. Any redemption of MRP Shares by the Fund will reduce any leverage applicable to the Common Shares.

Liquidation Preference

In the event of any voluntary or involuntary liquidation, dissolution or winding up of the Fund, the holders of MRP Shares will be entitled to receive a preferential liquidating distribution, equal to $25,000 per MRP Share plus accrued and unpaid dividends, whether or not declared, before any distribution of assets is made to Common Shareholders. After payment of the full amount of the liquidating distribution to which they are entitled, the holders of MRP Shares will not be entitled to any further participation in any distribution of assets by the Fund.

Voting Rights

The 1940 Act requires that the holders of any Preferred Shares, voting separately as a single class, have the right to elect at least two trustees at all times (the “Preferred Share Trustees”). The remaining trustees will be elected by holders of Common Shares and Preferred Shares, voting together as a single class. In connection with the issuance of the MRP Shares, Dan C. Tutcher and Alfred J. Moran were designated by the Board of Trustees as the Preferred Share Trustees of the Fund. Holders of the MRP Shares, and not Common Shareholders, will be entitled to vote on the election of each Preferred Share Trustee at the scheduled shareholder meeting at which such Preferred Share Trustee’s term expires. In addition, the holders of any Preferred Shares have the right to elect a majority of the trustees of the Fund at any time that two years of dividends on any Preferred Shares are unpaid. The 1940 Act also requires that, in addition to any approval by the shareholders that might otherwise be required, the approval of the holders of a majority of any outstanding Preferred Shares, voting separately as a class, would be required to: (i) adopt any plan of reorganization that would adversely affect the Preferred Shares and (ii) take any action requiring a vote of security holders under Section 13(a) of the 1940 Act, including, among other things, changes in the Fund’s sub-classification as a closed-end investment company or changes in its fundamental investment restrictions. As a result of these voting rights, the Fund’s ability to take any such actions may be impeded. Except as otherwise indicated in this Prospectus and except as otherwise required by applicable law or the governing documents of the Fund, holders of MRP Shares will have equal voting rights with Common Shareholders (one vote per share, unless otherwise required by the 1940 Act) and will vote together with Common Shareholders as a single class.

The affirmative vote of the holders of a majority of the outstanding MRP Shares, voting as a separate class, will be required to amend, alter or repeal any of the preferences, rights or powers of holders of MRP Shares so as to affect materially and adversely such preferences, rights or powers, or to borrow or issue Preferred Shares that ranks equally or senior to the MRP Shares.

MRP Shares Dividends

The Fund pays dividends on the MRP Shares in accordance with the terms thereof. The holders of the MRP Shares shall be entitled to receive cumulative cash dividends, when, as and if authorized by the Board of Trustees from funds legally available for distribution. Dividend payment dates with respect to the MRP Shares shall be, with respect to each dividend period, the first business day of the month next following each dividend period. Dividends on MRP Shares are payable quarterly.

So long as the MRP Shares are rated on any date no less than “A” by Fitch (and no less than an equivalent of such ratings by some other rating agency), then the dividend rate will be equal to 4.29% per annum. If the lowest credit rating assigned on any date to the then outstanding MRP Shares by Fitch (or any other rating agency) is equal to one of the ratings set forth in the table below (or its equivalent by some other rating agency), the dividend rate applicable to such outstanding MRP Shares for such date will

be adjusted by adding the respective enhanced dividend amount (which shall not be cumulative) set opposite such rating to the applicable rate.

If no rating agency is rating the MRP Shares, the dividend rate (so long as no rating exists) applicable to the MRP Shares for such date shall be the rate equal to the applicable rate plus 4.0%, unless the dividend rate is the default rate, in which case the dividend rate shall remain the default rate.

The default rate is equal to applicable rate in effect on such calendar day, without adjustment for any credit rating change on the MRP Shares, plus 5% per annum. Subject to the certain cure provisions, a default period with respect to MRP Shares will commence on a date the Fund fails to pay the full amount of any dividends on the MRP Shares payable on the dividend payment date or the full amount of any redemption price payable on a mandatory redemption date.

Limitation on Common Share Distributions

So long as the MRP Shares are outstanding, Common Shareholders will not be entitled to receive any distributions unless (1) the Fund has paid all accumulated dividends due on the MRP Shares on or prior to the date of such distribution; (2) the Fund has redeemed the full number of MRP Shares required to be redeemed by any provision for mandatory redemption contained in the statement of preferences of the MRP Shares; (3) the Fund’s asset coverage would be at least 225%; and (4) the assets in the Fund’s portfolio have a value, discounted in accordance with guidelines set forth by each applicable rating agency, at least equal to the basic maintenance amount required by such rating agency under its specific rating agency guidelines, in each case, after giving effect to distributions.

Redemption

The terms of the MRP Shares provide that: (i) the Fund may redeem the MRP Shares at its option at the liquidation preference plus accrued and unpaid dividends and plus a make-whole premium; (ii) the Fund is required to redeem the MRP Shares upon failure to maintain certain asset coverage tests; and (iii) the Fund is required to redeem the MRP Shares on the term redemption date of September 22, 2026.

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An investment in the Fund is subject to investment risk, including the possible loss of the entire principal amount that you invest. See “Risks” beginning on page 65 of the accompanying Prospectus. Certain of these risks are summarized in “Prospectus Summary—Special Risk Considerations” beginning on page 13 of the accompanying Prospectus. You should carefully consider these risks together with all of the other information contained in the Prospectus Supplement and the accompanying Prospectus before making a decision to purchase Common Shares.

Neither the SEC nor any state securities commission has approved or disapproved of these securities or determined if the Prospectus Supplement and the accompanying Prospectus is truthful or complete. Any representation to the contrary is a criminal offense.