Amendment to 2005 Stock Incentive Plan

Exhibit 10.1

1. Section 1 of the Plan shall be amended to add a reference to director participation in the Plan, and shall read in its entirety as follows:

     1. Purpose. The purpose of the 2005 Stock Incentive Plan (this “Plan”) of Horizon Offshore, Inc. (“Horizon”) is to increase stockholder value and to advance the interests of Horizon and its subsidiaries (collectively, the “Company”) by furnishing a variety of equity incentives (the “Incentives”) designed to attract, retain and motivate officers, employees, directors, consultants and advisors and to strengthen the mutuality of interests between such persons and Horizon’s stockholders. Incentives may consist of options to purchase shares of Horizon’s common stock (the “Common Stock”), stock appreciation rights, shares of restricted stock, restricted stock units or other stock-based awards, the value of which is based upon the value of the Common Stock, all on terms determined under this Plan. As used in this Plan, the term “subsidiary” means any corporation, limited liability company or other entity of which Horizon owns (directly or indirectly) within the meaning of Section 424(f) of the Internal Revenue Code of 1986, as amended (the “Code”), 50% or more of the total combined voting power of all classes of stock, membership interests or other equity interests issued thereby.

2. Section 2.2 shall be amended to delete the last sentence.

3. Section 3 shall be amended to add the following sentence to the end of the paragraph:

Directors who are not also employees of the Company (“Outside Directors”) may participate in the Plan only as specifically provided in Section 12 hereof.

4. The first sentence of Section 4.5(a) shall be amended to delete the reference to Section 4 and shall read in its entirety as follows:

In the event of any recapitalization, reclassification, stock dividend, stock split, combination of shares or other change in the Common Stock, all limitations on numbers of shares of Common Stock provided in this Plan and the number of shares of Common Stock subject to outstanding Incentives shall be equitably adjusted in proportion to the change in outstanding shares of Common Stock.

5. New Section 12 shall be added to the Plan, and shall read in its entirety as follows:

12. Stock Options for Outside Directors

12.1 Grant of Options. Outside Directors shall receive the following:

     (a) Each Outside Director shall be automatically granted non-qualified stock options to purchase 250,000 shares of Common Stock on the 21st calendar day after mailing an information statement in accordance with Rule 14c-2(b) under the 1934 Act; and

     (b) On the day following each annual meeting of stockholders of Horizon occurring after December 31, 2005, each Outside Director shall be automatically granted non-qualified stock options to purchase up to 250,000 shares of Common Stock, the exact number of which shall be set by the Board of Directors.

     12.2 Exercisability of Stock Options. Subject to the Committee’s right to accelerate the exercisability of any stock option and subject to the Committee’s rights under Section 11.12, the stock options granted to Outside Directors under this Section 12 shall be exercisable one year after the date of grant and shall expire ten years following the date of grant.

     12.3 Exercise Price. The exercise price of the stock options granted to Outside Directors shall be equal to the Fair Market Value, as defined in the Plan, of a share of Common Stock on the date of grant.

The exercise price may be paid as provided in Section 5.5 hereof.

     12.4 Exercise After Termination of Board Service. In the event an Outside Director ceases to serve on the Board, the stock options granted hereunder must be exercised, to the extent otherwise exercisable at the time of termination of Board service, within one year from termination of Board service; provided, however, that in the event of termination of Board service as a result of retirement (at age 65 or later or after having completed five or more years of service on the Board), the stock options may be exercised within five years from the date of termination of Board service. Notwithstanding the foregoing, no stock options may be exercised later than ten years after the date of grant.