Swiss pharmaceutical giant Roche Holding AG expects as many as five of its drugs will be approved by China in the next two years as the government accelerates the roll-out of new medicines to meet demand from a rapidly aging population.

“China is taking the political decision to spend more for health care,” Chairman Christoph Franz said in an interview at the China International Import Expo in Shanghai on Nov. 6. “Chinese consumers are sophisticated, and you are expecting that...