Starbucks has a China problem: coffee and tea drinkers who want more for less.

Vivian Yan tried her first Starbucks coffee eight years ago. She was desperate for a jolt of caffeine at work, and the store was nearby. “It didn’t necessarily mean I love Starbucks,” she said, “nor was it my first choice.”

These days, she thinks a cup of Starbucks is a little too expensive and prefers to get her coffee from McDonald’s. But what she really loves is ChaGee, HeyTea and other Chinese chains that sell coconut milk lattes, boba milk teas with cheese cream and sugary jasmine tea frappés. “They are delicious and offer more choices,” said Ms. Yan, 35, who is from China’s eastern province of Jiangsu.

Ms. Yan’s preference for more diverse flavors poses an acute challenge for Starbucks. It is losing customers at a rapid pace. Brian Niccol, the new chief executive, sounded the alarm in October, calling the competition “extreme” in the company’s second-biggest market behind the United States.

When Starbucks opened its first shop in China in 1999, tea dominated and coffee culture was practically nonexistent. But the company quickly built a thriving market alongside a swelling middle class that was turning to iPhones, Gucci handbags and other international brands to signal its newfound wealth.

Today, consumers are less interested in foreign brands, more cost conscious and enticed by local rivals that are popping up on corners all around the country offering something a little different. Dozens of competitors to Starbucks spin out new flavors of tea and coffee every week, at lower prices, creating competition so ferocious that Starbucks saw a 14 percent plunge in same-store sales in China in its most recent financial quarter.