Exhibit 5.1

Hogan Lovells US LLP

Harbor East

100 International Drive

Suite 2000

Baltimore, MD 21202

T +1 410 659 2700

F +1 410 659 2701

www.hoganlovells.com

December 6, 2017

Board of Directors

Capstead Mortgage Corporation

8401 North Central Expressway

Suite 800

Dallas, TX 75225-4410

At the Market Offerings of Common and Series E Preferred Stock

Ladies and Gentlemen:

We are acting as counsel to Capstead Mortgage Corporation, a Maryland corporation (the “Company”), in connection with its filing of a registration statement on Form S-3 (the “Registration Statement”), filed with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Act”), and the proposed offering of up to 15,000,000 shares of Common Stock, par value $0.01 per share, of the Company (the “Common Stock”) and up to 3,000,0000 shares of 7.50% Series E Cumulative Redeemable Preferred Stock, par value $.10 per share, of the Company (the “Preferred Stock” and, collectively with the Common Stock, the “Securities”). The Securities will be issued from time to time pursuant to a Sales Agreement dated as of December 6, 2017, by and between the Company and IFS Securities, Inc. (dba Brinson Patrick, a division of IFS Securities, Inc.) (the “Sales Agreement”). An undetermined number of shares of the Company’s Common Stock are issuable upon conversion of the Preferred Stock (the “Conversion Common Shares”). This opinion letter is furnished to you at your request to enable you to fulfill the requirements of Item 601(b)(5) of Regulation S-K, 17 C.F.R. § 229.601(b)(5), in connection with the Registration Statement.

For purposes of this opinion letter, we have examined copies of such agreements, instruments and documents as we have deemed an appropriate basis on which to render the opinions hereinafter expressed. In our examination of the aforesaid documents, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, the accuracy and completeness of all documents submitted to us, the authenticity of all original documents, and the conformity to authentic original documents of all documents submitted to us as copies (including telecopies). We also have assumed that the Securities will not be issued in violation of the ownership limit contained in the Company’s charter. As to all matters of fact, we have relied on the representations and statements of fact made in the documents so reviewed, and we have not independently established the facts so relied on. This opinion letter is given, and all statements herein are made, in the context of the foregoing.

Board of Directors

December 6, 2017

Page 2

This opinion letter is based as to matters of law solely on the Maryland General Corporation Law, as amended and as currently in effect. We express no opinion herein as to any other laws, statutes, ordinances, rules, or regulations.

Based upon, subject to and limited by the foregoing, we are of the opinion that;

(1) The Common Stock, if and when issued in accordance with the terms of the Sales Agreement, will be validly issued, fully paid and non-assessable.

(2) The Preferred Stock, if and when issued in accordance with the terms of the Sales Agreement, will be validly issued, fully paid and non-assessable.

(3) The Conversion Common Shares, if and when issued upon exercise of the conversion rights in accordance with the terms of the Preferred Stock, will be validly issued, fully paid and non-assessable.

This opinion letter has been prepared for use in connection with the Registration Statement. We assume no obligation to advise you of any changes in the foregoing subsequent to the effective date of the Registration Statement

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Current Report on Form 8-K related to the public offering of the Securities. In giving this consent, we do not thereby admit that we are an “expert” within the meaning of the Securities Act of 1933, as amended.

Very truly yours,

/s/ Hogan Lovells US LLP

HOGAN LOVELLS US LLP