Exhibit 5.1

Ref: VSL/742877-000002/19157993v1

Canaan Inc.

1-2/F, QianFang Science Building C

Building No. 27, Zhongguancun Software Park (Phase I)

No. 8 Dongbeiwang West Road

Haidian District, Beijing, 100193

People’s Republic of China

23 April 2021

Dear Sirs

Canaan Inc. (the “Company”)

We have acted as Cayman Islands legal counsel to the Company in connection with a registration statement on Form S-8 to be filed with the Securities and Exchange Commission (the “Commission”) on 23 April 2021 (the “Registration Statement”) relating to the registration under the United States Securities Act of 1933, as amended, (the “Securities Act”) of class A ordinary shares, par value US$0.00000005 per share (the “Shares”), issuable pursuant to the Amended and Restated 2018 Share Incentive Plan of the Company (the “Share Incentive Plan”).

For the purposes of giving this opinion, we have examined copies of the Registration Statement and the Share Incentive Plan. We have also reviewed copies of the amended and restated memorandum and articles of association of the Company adopted by special resolution passed on 4 October 2019 and effective immediately prior to the completion of the Company’s initial public offering of American Depositary Shares representing its Shares (the “Memorandum and Articles”), the written resolutions of the board of directors of the Company dated 4 October 2019 and 20 April 2021 (together, the “Resolutions”).

Based upon, and subject to, the assumptions and qualifications set out below, and having regard to such legal considerations as we deem relevant, we are of the opinion that:

1. The Shares to be issued by the Company and registered under the Registration Statement have been duly and validly authorized.

2. When issued and paid for in accordance with the terms of the Share Incentive Plan and in accordance with the Resolutions, and when appropriate entries are made in the register of members (shareholders) of the Company, the Shares will be validly issued, fully paid and non-assessable.

In this opinion letter, the phrase “non-assessable” means, with respect to the issuance of Shares, that a shareholder shall not, in respect of the relevant Shares and in the absence of a contractual arrangement, or an obligation pursuant to the memorandum and articles of association, to the contrary, have any obligation to make further contributions to the Company’s assets (except in exceptional circumstances, such as involving fraud, the establishment of an agency relationship or an illegal or improper purpose or other circumstances in which a court may be prepared to pierce or lift the corporate veil).

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These opinions are subject to the qualification that under the Companies Act (As Revised) of the Cayman Islands (the “Companies Act”), the register of members of a Cayman Islands company is by statute regarded as prima facie evidence of any matters which the Companies Act directs or authorises to be inserted therein. A third party interest in the shares in question would not appear. An entry in the register of members may yield to a court order for rectification (for example, in the event of fraud or manifest error).

These opinions are given only as to, and based on, circumstances and matters of fact existing and known to us on the date of this opinion letter. These opinions only relate to the laws of the Cayman Islands which are in force on the date of this opinion letter. We express no opinion as to the meaning, validity or effect of any references to foreign (i.e. non-Cayman Islands) statutes, rules, regulations, codes, judicial authority or any other promulgations.

We have also relied upon the assumptions, which we have not independently verified, that (a) all signatures, initials and seals are genuine, (b) copies of documents, conformed copies or drafts of documents provided to us are true and complete copies of, or in the final forms of, the originals, (c) upon the issue of any Shares, the consideration received by the Company shall be not less than the par value of such Shares, and (d) there is nothing contained in the minute book or corporate records of the Company (which we have not inspected) which would or might affect the opinions set out above.

This opinion letter is to and for the benefit solely of the addressee and may not be relied upon by any other person for any purpose.

We consent to the use of this opinion as an exhibit to the Registration Statement and further consent to all references to us in the Registration Statement and any amendments thereto. In giving such consent, we do not consider that we are “experts” within the meaning of such term as used in the Securities Act, or the rules and regulations of the Commission issued thereunder, with respect to any part of the Registration Statement, including this opinion as an exhibit or otherwise.

Yours faithfully

/s/ Maples and Calder (Hong Kong) LLP

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