Exhibit 31.1



Certification Pursuant to Rule 13a-14(a) (17 CFR
240.13a-14(a))

or Rule 15d-14(a) (17 CFR 240.15d-14(a)) under the Securities
Exchange Act of 1934



I, Bill J. Lam, certify that:

| | 1. | I have reviewed this Amendment No. 2 to Annual Report on Form 10-K/A for
    the year 2003 of Horizon Offshore, Inc.;                                                                                                                                                                                                 
| | -- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| |    |                                                                                                                                                                                                                                                                                                                       
| | 2. | Based on my knowledge, this report does not contain any untrue statement
    of a material fact or omit to state a material 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 maintaining disclosure controls and procedures (as defined
    in Exchange Act Rules 13a-15(e) and 15d-15(e)) for the registrant and have:                                                                                
| |    |                                                                                                                                                                                                                                                                                                                       
| |    | a.                                                                                                                                                                                                                                                                                                                    
| |    |                                                                                                                                                                                                                                                                                                                       
| |    | b.                                                                                                                                                                                                                                                                                                                    
| |    |                                                                                                                                                                                                                                                                                                                       
| |    | c.                                                                                                                                                                                                                                                                                                                    
| |    |                                                                                                                                                                                                                                                                                                                       
| | 5. | The registrant's other certifying officer(s) and I have disclosed, based
    on our most recent evaluation of internal 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.                                                                                                                                                                                                                                                                                                                    
| |    |                                                                                                                                                                                                                                                                                                                       
| |    | b.                                                                                                                                                                                                                                                                                                                    
| |    |                                                                                                                                                                                                                                                                                                                       

Dated: June 30, 2004

| | /s/ Bill J. Lam                                                                    
| | -----------------------------------------------------------------------------------
| | Bill J. Lam
		President and Chief Executive Officer
		(Principal Executive Officer)