Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the registration statement on Form S-8 (File No. 333-252103) of our report, dated March 18, 2022 on our audits of the consolidated financial statements of Compass Therapeutics, Inc. and subsidiaries as of December 31, 2021 and 2020 and for the years then ended, included in this Annual Report on Form 10-K of Compass Therapeutics, Inc. for the year ended December 31, 2021.

/s/ CohnReznick LLP

Melville, New York

March 18, 2022