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**Exhibit 31.1**

**Certification Pursuant to Rule 13a-14(a) of the Securities Exchange Act of 1934**

I, Harold H. Shlevin, Ph.D., certify that: 

 
1.
I have reviewed this annual report on Form 10-K of Galectin Therapeutics Inc.; 

 
2.
Based on my knowledge, this report does not contain any untrue statement of a material fact or omit to state amaterial fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this report; 

 
3.
Based on my knowledge, the financial statements, and other financial information included in this report,fairly present in all material respects the financial condition, results of operations and cash flows of the registrant as of, and for, the periods presented in this report; 

 
4.
The registrant’s other certifying officer(s) and I are responsible for establishing and maintainingdisclosure controls and procedures (as defined in Rule 30a-3(c) under the Investment Company Act of 1940) and internal control over financial reporting (as defined in Rule 30a-3(d) under the Investment Company Act of 1940) for the registrant andhave: 

 
 a)
Designed such disclosure controls and procedures, or caused such disclosure controls and procedures to bedesigned under our supervision, to ensure that material information relating to the registrant, including its consolidated subsidiaries, is made known to us by others within those entities, particularly during the period in which this report isbeing prepared; 

 
 b)
Designed such internal control over financial reporting, or caused such internal control over financialreporting to be designed under our supervision, to provide reasonable assurance regarding the reliability of financial reporting and the preparation of financial statements for external purposes in accordance with generally accepted accountingprinciples; 

 
 c)
Evaluated the effectiveness of the registrant’s disclosure controls and procedures and presented in thisreport our conclusions about the effectiveness of the disclosure controls and procedures, as of the end of the period covered by this report based on such evaluation; and 

 
 d)
Disclosed in this report any change in the registrant’s internal control over financial reporting thatoccurred during the registrant’s most recent fiscal quarter (the registrant’s fourth fiscal quarter in the case of an annual report) that has materially affected, or is reasonably likely to materially affect, the registrant’s internalcontrol over financial reporting; and 

 
5.
The registrant’s other certifying officer and I have disclosed, based on our most recent evaluation ofinternal control over financial reporting, to the registrant’s auditors and the audit committee of the registrant’s board of directors (or persons performing the equivalent functions): 

 
 a)
All significant deficiencies and material weaknesses in the design or operation of internal control overfinancial reporting which are reasonably likely to adversely affect the registrant’s ability to record, process, summarize and report financial information; and 

 
 b)
Any fraud, whether or not material, that involves management or other employees who have a significant role inthe registrant’s internal control over financial reporting. 

 
Date: September 28, 2018   /s/ Harold H. Shlevin, Ph.D.  Name: Harold H. Shlevin, Ph.D.  Title: 
Chief Executive Officer and President

(principal executive officer)
**