UNITED STATES

SECURITIES AND EXCHANGECOMMISSION

WASHINGTON, D.C. 20549

FORM 6-K

REPORT OF FOREIGN PRIVATEISSUER

PURSUANT TO RULE 13a-16OR 15d-16 UNDER THE

SECURITIES EXCHANGEACT OF 1934

For the month of October2025

Commission File Number:001-39127

Canaan Inc.

28 Ayer Rajah Crescent

#06-08

Singapore 139959

(Address of principalexecutive offices)

Indicate by check mark whether the registrantfiles or will file annual reports under cover of Form 20-F or Form 40-F.

Form 20-F x            Form40-F ¨

EXHIBITS

SIGNATURE

Pursuant to the requirementsof the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereuntoduly authorized.

Date: October 31, 2025

Exhibit 99.1

Canaan Inc. ProvidesUpdates to At-the-Market Offering Program

ApproximatelyUS$7.8 million raised at an average price of approximately US$1.61 per ADS

Company to pausefurther ATM Sales through 2025

SINGAPORE, October31, 2025 /PRNewswire/ -- Canaan Inc. (NASDAQ: CAN) (“Canaan” or the “Company”), an innovator incrypto mining, today provides an update to its at-the-market (“ATM”) offering program.

On October 24,2025, Eastern Standard Time, the Company established a new ATM equity offering program to replace the previous program, which had expired.The renewal was intended to broaden Canaan’s banking relationships and enhance its financial flexibility for future growth initiatives.

Following the renewal,Canaan sold a total of approximately 4.84 million American depositary shares (“ADSs”) through the ATM program at a combinedaverage price of approximately US$1.61 per ADS, resulting in total gross proceeds of about US$7.8 million.

The Company hasceased any further sales under the program and does not plan to sell additional shares through the ATM for the remainder of 2025. Whetherand when to resume active sales in 2026 will depend on the Company’s cash requirements, market conditions and other relevant factors.

Canaan’scash position remains solid, supported by continued business momentum. As of September 30, 2025, Canaan held a cryptocurrency treasuryof 1,582 bitcoins and 2,830 ETH. On October 28, 2025, the Company introduced its latest generation bitcoin mining machine,the Avalon A16 series, featuring industry-leading power efficiency and manufacturing quality.

About CanaanInc.

Established in2013, Canaan Inc. (NASDAQ: CAN), is a technology company focusing on ASIC high-performance computing chip design, chip research and development,computing equipment production, and software services. Canaan has extensive experience in chip design and streamlined production in theASIC field. In 2013, Canaan's founding team shipped to its customers the world's first batch of mining machines incorporating ASIC technologyunder the brand name Avalon. In 2019, Canaan completed its initial public offering on the Nasdaq Global Market. To learn more about Canaan,please visit https://www.canaan.io/.

Safe HarborStatement

This press releasecontains forward-looking statements. These statements are made under the "safe harbor" provisions of the U.S. PrivateSecurities Litigation Reform Act of 1995. These forward-looking statements can be identified by terminology such as "will,""expects," "anticipates," "future," "intends," "plans," "believes," "estimates"and similar statements. Among other things, the business outlook and quotations from management in this announcement, as well as CanaanInc.'s strategic and operational plans, contain forward-looking statements. Canaan Inc. may also make written or oralforward-looking statements in its periodic reports to the U.S. Securities and Exchange Commission ("SEC") on Forms20-F and 6-K, in its annual report to shareholders, in press releases and other written materials and in oral statements made by itsofficers, directors or employees to third parties. Statements that are not historical facts, including statements about Canaan Inc.'s beliefsand expectations, such as expectations with regard to revenue or mining hash rate deployment, are forward-looking statements. Forward-lookingstatements involve inherent risks and uncertainties. A number of factors could cause actual results to differ materially from those containedin any forward-looking statement, including but not limited to the following: the Company's goals and strategies; the Company's futurebusiness development, the ability of the Company to execute against its goals, financial condition and results of operations; the expectedgrowth of the bitcoin industry and the price of bitcoin; the Company's expectations regarding demand for and market acceptanceof its products, especially its bitcoin mining machines; the Company's expectations regarding maintaining and strengtheningits relationships with production partners and customers; the Company's investment plans and strategies, fluctuations in the Company'squarterly operating results; competition in its industry; changing macroeconomic and geopolitical conditions, including evolving internationaltrade policies and the implementation of increased tariffs, import restrictions, and retaliatory trade actions; and relevant governmentpolicies and regulations relating to the Company and cryptocurrency. Further information regarding these and other risks is includedin the Company's filings with the SEC. All information provided in this press release and in the attachments is as of the date ofthis press release, and Canaan Inc. does not undertake any obligation to update any forward-looking statement, except as requiredunder applicable law.

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Investor Relations Contact

Canaan Inc.
Xi Zhang
Email: IR@canaan-creative.com

Christensen Advisory

Christian Arnell

Email: canaan@christensencomms.com