YOKOHAMA, Japan—The new head of Nissan Motor Co.’s luxury division, Infiniti, said Thursday that he would focus on improving customer service in a bid to close the yawning gap with the German premium brands that dominate the segment.

Roland Krueger, who took over as Infiniti president on Jan. 1, is the fourth executive to lead the brand in less than a year—a mark of the challenges facing the unit as it tries to catch up with BMW AG, Volkswagen AG’s Audi and Daimler AG’s Mercedes-Benz. Infiniti also trails a Japanese rival,...