Exhibit 5.1 and 23.1

Conyers Dill & Pearman Limited

26 May 2017

Matter No: 355438

Legal — 12558646.2

441-299-4993

Jason.Piney@conyersdill.com

Kosmos Energy Ltd.

Clarendon House

2 Church Street

Hamilton, HM 11

Bermuda

Dear Sirs,

Re: Kosmos Energy Ltd. (the “Company”)

We have acted as special Bermuda legal counsel to the Company in connection with an offering to be made pursuant to the prospectus (including the prospectus supplement, dated 22 May 2017 in the form filed pursuant to Rule 424(b), the “Prospectus”, 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) included in a registration statement on Form S-3 (the “Registration Statement”) filed with the U.S. Securities and Exchange Commission on 22 June 2015 under the U.S. Securities Act of 1933, as amended, relating to the sale by the selling shareholders identified in the Prospectus (the “Selling Shareholders”) of an aggregate of 40,000,000 common shares, par value US $0.01 each (the “Shares”).

For the purposes of giving this opinion, we have examined a copy of the Prospectus. We have also reviewed the memorandum of association and the bye-laws of the Company, each certified by the Assistant Secretary of the Company on 26 May 2017, an extract of minutes of a meeting of its directors held on 13 September 2016 certified by the Secretary of the Company on 18 May 2017 (the “Resolutions”) 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

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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 Prospectus and other documents reviewed by us, (d) that the Resolutions 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.

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 offering of the Common Shares by the Selling Shareholders 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:

1.              The Company is duly incorporated and existing under the laws of Bermuda in good standing (meaning solely that it has not failed to make any filing with any Bermuda government authority or to pay any Bermuda government fees or tax which would make it liable to be struck off the Register of Companies and thereby cease to exist under the laws of Bermuda).

2.              Based solely upon a review of the register of members of the Company dated 25 May 2017, prepared by Computershare Trust Company, N.A., the branch registrar of the Company, the Shares are 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 Company’s Current Report on Form 8-K filed on 26 May 2017 and to the references to our firm under the caption “Validity of Securities” in the prospectus forming a part of 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

Conyers Dill & Pearman Limited

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