Payments startup Square Inc. on Friday said it plans to raise up to $403.7 million in its initial public offering amid what has been a rocky IPO market.

The San Francisco company, known for its credit-card readers that attach to mobile devices, is run by Twitter Inc. co-founder and Chief Executive Jack Dorsey. Mr. Dorsey owns about a quarter of Square's stock.

Square said in a regulatory filing that it would sell 27 million shares at $11 to $13 a piece. Underwriters will have the option to buy an additional 4.05 million shares.

The offering comes in what has been a tough IPO market. Recent sharp stock-market swings have deterred some firms from pursuing public offerings, with one of the year's biggest IPOs—grocer Albertsons Companies Inc.—recently scrapping plans.

The Square offering is seen as a harbinger for technology companies valued at $1 billion or more—Square was valued by investors last fall at about $6 billion. Many highly valued companies, armed with private capital have stayed away from the IPO market. There were just 22 tech IPOs through the third quarter this year, compared with 53 through the third quarter of 2014, according to Dealogic.

Like many other Silicon Valley tech firms, Square has been posting growing sales but swelling losses. The company said sales rose 54% last year to $850.2 million and are on a pace to exceed $1 billion this year. Its loss, meanwhile, widened to $154.1 million last year from $104.5 million in 2013.

Including Mr. Dorsey's stake, venture-capital firm Khosla Ventures's 17.3% stake and smaller shares held by board members and executives, about two-thirds of Square is held by insiders.

Write to Lisa Beilfuss at lisa.beilfuss@wsj.com

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(END) Dow Jones Newswires

November 06, 2015 08:05 ET (13:05 GMT)