By Daisuke Wakabayashi 

Apple Inc.'s quarterly profit surged a better-than-expected 38% to a record high, sparked by booming demand for its bigger-screen iPhones.

After years of ceding the popular large smartphone market to competitors, Apple's iPhone 6 and iPhone 6 Plus made their debut 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. and 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 a share on revenue of $67.7 billion. In October, Apple had projected quarterly revenue of between $63.5 billion and $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.

In after-hours trading, Apple shares rose about 5%. Its shares were off $3.96 at $109.14 in 4 p.m. trading in New York. Over the past year, Apple shares have surged 40% in part on expectations of strong demand for the bigger phones.

On the company's conference call, Apple said it would ship its highly anticipated Apple Watch in April.

As Apple sells more iPhones than ever, it also is 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 also is 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.

Apple had predicted that the new iPhones would spark a huge upgrade cycle among its existing consumers. Chief Executive Tim Cook said in an interview on Tuesday that it is luring customers from rival smartphone manufacturers running the Android operating system.

"We brought on more new people to iPhone than ever before," Mr. Cook said. "Many of those are switching from Android, and we couldn't be happier about that."

Apple said its gross margin, a closely watched indicator measuring the percentage of revenue that remains after manufacturing costs, was 39.9% in the December quarter, above the 37.9% reported in the year period. In October, Apple had forecast gross margin of between 37.5% and 38.5% for the quarter.

For the current quarter ending March, Apple said it expects revenue of between $53 billion and $55 billion with gross margin of between 38.5% and 39.5%. Analysts had been forecasting revenue for the current quarter of $53.8 billion and a gross margin of 38.7%, according to Thomson Reuters.

Apple ended the quarter with $178 billion in cash.

Apple's iPhone sales provided cover for another sluggish quarter for the iPad. Apple said it sold 21.4 million iPads during the December period, an 18% decline from a year earlier. The sales were close to analysts' expectations.

On the other hand, the Mac personal computer fared well again. It has gained market share consistently against PC rivals in recent quarter. Apple said it sold 5.5 million Macs during the quarter, a 14% increase from a year earlier. Research firm IDC said overall PC shipments fell 2.4% during the fourth quarter. Competing researcher Gartner said quarterly shipments rose 1%.

In a quarter when Apple surpassed even the most bullish forecasts, the question hanging over the company is whether the strong iPhone 6 and iPhone 6 Plus sales are a one-time boost from pent-up demand for a bigger-display phone or whether Apple can maintain this momentum with the next batch of iPhones and new products such as the Apple Watch.

Apple said its new mobile payments service got off to strong start. The company said Apple Pay, which allows consumers to wave an iPhone near a wireless reader, accounted for two of every three dollars spent via contactless payments on Visa, MasterCard or American Express since its debut in October.

Apple Pay is being closely watched as a potential harbinger of a trend to paying for items using mobile devices. Apple didn't break out Apple Pay in its results.

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

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