EXHIBIT 32.1

CERTIFICATION OF JOHN M. ANZALONE

PURSUANT TO

18 U.S.C. SECTION 1350

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with Invesco Mortgage Capital Inc.’s (the “Company”) Quarterly Report on Form 10-Q for the period ended June 30, 2019 (the “Report”), I, John M. Anzalone, do hereby certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 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.

August 7, 2019

/s/ John M. Anzalone

John M. Anzalone

Chief Executive Officer