Exhibit 5.1 Dentons US LLP 303 Peachtree Street, NE • Suite 5300 Atlanta, GA 30308-3265 United States   dentons.com

May 11, 2020

Board of Directors

Galectin Therapeutics Inc.

4960 Peachtree Industrial Blvd., Suite 240

Norcross, Georgia 30071

Re: Registration Statement on Form S-3

Gentlemen:

We have acted as counsel to Galectin Therapeutics Inc., a Nevada corporation (the “Company”) in connection with the preparation of a registration statement on Form S-3 (the “Registration Statement”), that is to be filed on or about the date hereof with the United States Securities and Exchange Commission (the “Commission”) under the United States Securities Act of 1933, as amended (the “Securities Act”) and the rules and regulations promulgated thereunder (the “Rules”), relating to the proposed offer, issuance and sale from time to time by the Company of up to $100,000,000 of any combination of the following securities (collectively, the “Securities”):

(a)    shares of the Company’s common stock, par value $0.001 per share (the “Common Stock”), including, but not limited to, shares of the Company’s Common Stock having an aggregate offering price of up to $40,000,000 (the “ATM Common”) that may be issued pursuant to and under the Company’s At The Market Issuance Sales Agreement (the “ATM Agreement”) with H.C. Wainwright & Co., LLC (“Wainwright”);

(b)    warrants to purchase shares of Common Stock (“Warrants”);

(c)    rights to purchase shares of Common Stock (“Rights”); and

(d)    such indeterminate number of shares of Common Stock, Warrants and Rights that may be issued upon the exercise of Warrants or Rights (collectively, “Indeterminate Securities”).

The Securities will be sold or delivered from time to time in amounts, at prices and on terms to be determined at the time of the offering as set forth in the Registration Statement, any amendments thereto, and each prospectus contained therein (each, a “Prospectus”) and supplements to each Prospectus (each, a “Prospectus Supplement”).

This opinion letter is being rendered pursuant to Item 16 of Form S-3 and Item 601(b)(5) of Regulation S-K.

We have reviewed such documents and made such examination of law as we have deemed appropriate to give the opinions contained within this opinion letter and set forth below. We have relied, without independent verification, on certificates of public officials and, as to matters of fact material to the opinions set forth below, and on certificates of officers of the Company.

Our opinions as set forth in this opinion letter are limited to Nevada corporate law (which includes the applicable provisions of Chapter 78 of the Nevada Revised Statutes and the reported judicial decisions interpreting those laws) and the federal laws of the United States of America, to the extent referred to specifically herein. We do not express any opinion herein concerning any other laws. We are generally familiar with Chapter 78 of the Nevada Revised Statutes as currently in effect and the judicial decisions thereunder and have made such inquiries and review

Dentons US LLP 303 Peachtree Street, NE • Suite 5300 Atlanta, GA 30308-3265 United States   dentons.com

of matters of fact and law as we determined necessary to render the opinion contained herein. We assume no obligation to revise or supplement this opinion in the event of future changes in such laws or the interpretations thereof or such facts. We express no opinion regarding the Securities Act, or any other federal or state laws or regulations.

For purposes of the Base Shelf Opinions (as defined below) herein, without limiting any other exceptions or qualifications set forth herein, we have assumed that after the issuance of any Securities (other than any ATM Common) offered pursuant to the Registration Statement, the total number of issued shares of Common Stock, together with the total number of shares of such Common Stock issuable upon the exercise, exchange, conversion or settlement, as the case may be, of any exercisable, exchangeable or convertible security (including without limitation any Warrants or Rights), as the case may be, then outstanding, will not exceed the total number of authorized shares of Common Stock under the Company’s Amended and Restated Articles of Incorporation, as amended (the “Charter”).

For purposes of the Base Shelf Opinions set forth below, we refer to the following as the “Future Authorization and Issuance”:

• with respect to any of the Securities, (a) the authorization by the Company of the amount, terms and issuance of such Securities (the “Authorization”) and (b) the issuance of such Securities in accordance with the Authorization therefor upon the receipt by the Company of the consideration (which, in the case of shares of Common Stock is not less than the par value of such shares) to be paid therefor in accordance with the Authorization; and

• with respect to Warrants or Rights, (a) the authorization, execution and delivery by the Company and the other parties thereto of any agreement under which such Securities are to be issued and (b) the establishment of the terms of such Securities, and the execution and delivery of such Securities, in conformity with any applicable agreement under which such Securities are to be issued and applicable law.

Based upon the foregoing, and subject to the additional qualifications set out within this opinion letter, we are of the opinion that (the following opinions collectively, the “Base Shelf Opinions”):

1. Upon the Future Authorization and Issuance of shares of Common Stock (excluding the ATM Common, but including, for the avoidance of doubt, any Indeterminate Securities), such shares of Common Stock will be validly issued, fully paid and nonassesable.

2. Upon the Future Authorization and Issuance of Warrants (including any Indeterminate Securities), such Warrants will be valid and binding obligations of the Company.

3. Upon the Future Authorization and Issuance of Rights (including any Indeterminate Securities), such Rights will be valid and binding obligations of the Company.

Base Shelf Opinions No. 2 and 3 above are subject to bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and other similar laws of general application affecting the rights and remedies of creditors and to general principles of equity.

In addition to the Base Shelf Opinions above, we are delivering the below supplemental opinion in connection with the Prospectus Supplement contained within the Registration Statement (the “ATM Prospectus Supplement”) that relates to the shares of ATM Common that are being offered and sold by the Company through Wainwright pursuant to and in accordance with the ATM Agreement.

Dentons US LLP 303 Peachtree Street, NE • Suite 5300 Atlanta, GA 30308-3265 United States   dentons.com

For purposes of the supplemental opinion set forth below, we have assumed that the ATM Common is issued for a price per share equal to or greater than the minimum price authorized by the Company’s board of directors prior to the date hereof (the “Minimum Price”) and that no event occurs that causes the number of authorized shares of Common Stock available for issuance by the Company under the Charter to be less than the number of then-unissued shares of ATM Common that may be issued for the Minimum Price.

Based on the foregoing, we are of the opinion that the ATM Common will be validly issued, and that, upon receipt by the Company of the consideration (which shall not be less than the par value of each such share of ATM Common), the ATM Common will be fully paid and nonassessable.

This opinion letter is provided for use solely in connection with the offer, issuance and sale of the Securities while the Registration Statement is in effect, and except for its use in connection with such offer, issuance and sale, may not be furnished to, quoted from or relied upon by any other person, firm, or corporation without our express written consent. No opinion may be implied or inferred beyond the opinion expressly stated in the opinion paragraphs contained above, which, for the avoidance of doubt, begin with the phrase “we are of the opinion that”. Our opinions expressed herein are as of the date hereof, and we undertake no obligation to advise you of any changes in applicable law or any other matters that may come to our attention after the date hereof that may affect our opinions expressed herein.

We consent to the filing of this opinion letter as an exhibit to the Registration Statement and to the use of our name under the heading “Legal Matters” in the prospectus constituting a part thereof. In giving such consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the Rules of the Commission thereunder.

Very truly yours,

/s/ Dentons US LLP

Dentons US LLP