In a lean-burn engine equipped with a turbocharger, a responsiveness of a supercharging pressure in a lean region is enhanced by control of a valve timing of an exhaust valve while a combustion state is restrained from varying. A variable valve mechanism that can change an opening timing of the exhaust valve while keeping a closing timing of the exhaust valve constant, is included in the lean-burn engine. When a target operation point is located in the lean region, and when an actual supercharging pressure is lower than a target supercharging pressure, supercharging pressure increasing control that advances the opening timing while keeping the closing timing constant is executed by operating the variable valve mechanism.