Exhibit 5.1

14 March 2019

Matter No.: 475109

Doc Ref: 15280223

441 299 4938

guy.cooper@conyersdill.com

Kosmos Energy Ltd.

8176 Park Lane

Dallas, Texas

United States of America

Dear Sirs,

Kosmos Energy Ltd. (the "Company")

We have acted as special Bermuda legal counsel to the Company, a company incorporated in Delaware, in connection with a registration statement on form S3 filed with the U.S. Securities and Exchange Commission (the "Commission") on 14 March 2019 (the "Registration Statement", which term does not include any other document or agreement whether or not specifically referred to therein or attached as an exhibit or schedule thereto) relating to the registration under the U.S. Securities Act of 1933, as amended, (the "Securities Act") of an aggregate of 34,993,585 common shares, par value US$0.01 each of the Company (the "Common Shares"), which were issued as “Parent Common Equity” pursuant to, and as such term is defined in, a Securities Purchase Agreement dated 3 August 2018 between, inter alios, DGE Group Series Holdco, LLC and Kosmos Energy Gulf of Mexico, LLC (the “Securities Purchase Agreement”) on 14 September 2018 when the Company was duly incorporated and existing under the laws of Bermuda. The Company discontinued as an exempted company incorporated in Bermuda on 28 December 2018 and continued to Delaware.

For the purposes of giving this opinion, we have examined a copy of the Registration Statement. We have also reviewed the memorandum of association and the bye-laws of the Company and an excerpt of minutes of a meeting of its board of directors held on 3 August 2018 (the “Minutes”), each certified by the Secretary of the Company on 12 September 2018, and such other documents and made such enquiries as to questions of law as we have deemed necessary in order to render the opinion set forth below.

We have assumed (a) the genuineness and authenticity of all signatures and the conformity to the originals of all copies (whether or not certified) examined by us and the authenticity and completeness of the originals from which such copies were taken, (b) that where a document has been examined by us in draft form, it will be or has been executed and/or filed in the form of that draft, and where a number of drafts of a document have been examined by us all changes thereto have been marked or otherwise drawn to our attention, (c) the accuracy and completeness of all factual representations made in the Registration Statement, Securities Purchase Agreement and other documents reviewed by us, (d) that the resolutions contained in the Minutes were passed at one or more duly convened, constituted and quorate meetings, or by unanimous written resolutions, remain in full force and effect and have not been rescinded or amended, (e) that there is no provision of the law of any jurisdiction, other than Bermuda, which would have any implication in relation to the opinions expressed herein, (f) that upon issue of the Common Shares the Company received consideration for the full issue price thereof which shall be equal to at least the par value thereof, and (g) that on the date of issue of the Common Shares pursuant to the Securities Purchase Agreement, the Company was able to pay its liabilities as they became due.

We have made no investigation of and express no opinion in relation to the laws of any jurisdiction other than Bermuda. This opinion is to be governed by and construed in accordance with the laws of Bermuda and is limited to and is given on the basis of the current law and practice in Bermuda. This opinion is issued solely for the purposes of the filing of the Registration Statement and is not to be relied upon in respect of any other matter.

On the basis of and subject to the foregoing, we are of the opinion that:

Based solely upon a review of the register of members of the Company dated 14 September 2018, prepared by Computershare Trust Company, N.A., the branch registrar of the Company, the Common Shares were validly issued, fully paid and non-assessable (which term means when used herein that no further sums are required to be paid by the holders thereof in connection with the issue of such shares).

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement. In giving this consent, we do not hereby admit that we are experts within the meaning of Section 11 of the Securities Act or that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the Rules and Regulations of the Commission promulgated thereunder.

Yours faithfully,

/s/ Conyers Dill & Pearman Limited

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