Apple Inc. said quarterly profit rose 38% to a record high, sparked by booming demand for its new bigger-screen iPhones.

After years of ceding the popular large smartphone market to competitors, Apple's iPhone 6 and iPhone 6 Plus debuted in September to consumers hungry for a bigger display phone from the Cupertino, Calif., technology giant. Apple encountered supply shortages for weeks in traditional strongholds like the U.S., as well as fast-growing markets like China.

Apple posted net income of $18.0 billion for its fiscal first quarter ended Dec. 27, up from $13.1 billion in the same period a year earlier. Earnings per share rose 48% to $3.06 from a split-adjusted $2.07. Revenue increased 30% to $74.6 billion from $57.6 billion.

Analysts polled by Thomson Reuters estimated that Apple would post earnings of $2.60 per share on revenue of $67.7 billion. In October, Apple had projected quarterly revenue of $63.5 billion to $66.5 billion.

The earnings were driven by record iPhone sales. Apple said it sold 74.5 million iPhones during the quarter, up 46% from a year ago and above analysts' estimates for 66.5 million units. Strong iPhone sales helped Apple claw back market share that it gave up to Samsung Electronics Co. in the past three years.

As Apple sells more iPhones than ever, it's also selling more expensive phones. The average selling price of the iPhone was $687 in the quarter compared with $637 in the year-ago period. The iPhone 6 Plus costs $100 more than Apple's previous high-end model. Plus Apple is also enticing consumers to upgrade to more expensive models with greater memory.

Apple's performance was especially impressive in China, where it surged to become the top smartphone manufacturer during the quarter, according to research firm Canalys. It also gained market share against phones using Google Inc.'s Android operating system in the U.S., Germany, Great Britain, Australia and Spain for the three months ended November, said Kantar Worldpanel ComTech earlier this month.

Write to Daisuke Wakabayashi at Daisuke.Wakabayashi@wsj.com

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