Cheniere Corpus Christi 10-Q 2021 Q1 Quarterly report

Exhibit 32.1

CERTIFICATION BY PRESIDENT AND CHIEF FINANCIAL OFFICER

PURSUANT TO 18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the quarterly report of Cheniere Corpus Christi Holdings, LLC (the “Company”) on Form 10-Q for the quarter ended March 31, 2021, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Zach Davis, President and Chief Financial Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, to my knowledge, that:

(1)    The Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2)    The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: May 3, 2021

/s/ Zach Davis

Zach Davis

President and Chief Financial Officer of

Cheniere Corpus Christi Holdings, LLC