Volkswagen AG set plans to list its heavy-truck division Traton SE in Frankfurt and Stockholm, moving forward with one of the year’s largest European public offerings despite a wobbly stock market and a swirling trade war between China and the U.S.

The company reaffirmed it expects the IPO to be completed “before the summer break” for German factories, while a person familiar with the matter said it could get done within four weeks. VW envisions the sale of between 10% and 25% of Traton, with the first step expected to be in the mid to lower end of that range,...