Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We have issued our report dated March 19, 2020 with respect to the consolidated financial statements of Moleculin Biotech, Inc. incorporated by reference from the Annual Report on Form 10-K for the year ended December 31, 2019 in the Registration Statement on Form S-3, as amended (File No. 333-235686), which are incorporated by reference in this Registration Statement on Form S-3MEF. We consent to the incorporation by reference of the aforementioned report in this Registration Statement, and to the use of our name as it appears under the caption "Experts" in the prospectus incorporated by reference in this Registration Statement.

/s/GRANT THORNTON LLP

Houston, Texas

February 2, 2021