EXHIBIT 32.1

GREAT AJAX CORP.

CERTIFICATION PURSUANT TO

18 U.S.C. §1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Annual Report of Great Ajax Corp. (the “Company”) on Form 10‑K for the period ended December 31, 2018 as filed with the Securities and Exchange Commission (the “Report”), I, Lawrence Mendelsohn, Chief Executive Officer of the Company, hereby certify as of the date hereof, pursuant to 18 U.S.C. § 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

(1) the Report fully complies with the requirements of Section 13(a) or 15(d), as applicable, 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 at the dates and for the periods indicated.

This Certification has not been, and shall not be deemed, “filed” with the Securities and Exchange Commission.

Dated: March 6, 2019

/s/ Lawrence Mendelsohn

Lawrence Mendelsohn

Chief Executive Officer