Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in this Post-Effective Amendment No. 1 on Form S-3 Registration Statement (No. 333-209513) of Great Ajax Corp. of our report dated March 29, 2016, relating to the consolidated financial statements of Great Ajax Corp., appearing in its Annual Report on Form 10-K for the year ended December 31, 2015, filed with the Securities and Exchange Commission, and to the reference to our firm under the heading “Experts” in the Prospectus, which is part of this Registration Statement.

/s/ Moss Adams LLP

Portland, Oregon

April 12, 2016