BEIJING—China’s stock market was swooning. Investors were panicking. Yet when Chinese President Xi Jinping spoke that first Monday in January, he didn’t address the global angst about the world’s second-largest economy.

Clad in an olive-green Mao suit, he was talking instead to Chinese troops about another challenge that consumes his time and political capital: the biggest restructuring of the People’s Liberation Army since the 1950s, a plan that unnerves America and its Asian allies and could upset the global balance of power.

“We must emancipate our minds and change with the times,” he told troops of the 13th Group Army on Jan. 4. They should not, he said, “wear new shoes to walk the old road.”

Four days earlier, Mr. Xi had started to implement a plan to transform the Soviet-modelled military, long focused on defending China from invasion, into a smaller, modern force capable of projecting power far from its shores.

The plan, to be implemented by 2020, is one of Mr. Xi’s most ambitious and politically risky undertakings yet.