Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in this Registration Statement of Compass Therapeutics, Inc. on Form S-3 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, which report is included in the Annual Report on Form 10-K of Compass Therapeutics, Inc. for the year ended December 31, 2021. We also consent to the reference to our firm under the caption "Experts."

/s/ CohnReznick LLP

Melville, New York

December 2, 2022