WASHINGTON—Negotiators for the U.S. and China have scheduled a new round of high-level trade talks in Beijing and Washington, aiming to close a deal by late April to end the yearlong dispute between the world’s two largest economies.

U.S. Trade Representative Robert Lighthizer and Treasury Secretary Steven Mnuchin plan to fly to Beijing next week to meet with Chinese Vice Premier Liu He, Trump administration officials said. The following week, a Chinese delegation led by Mr. Liu is expected to continue talks in Washington,...