An engine having a cylinder, a piston slideably received in the cylinder, a crankshaft connected to the piston, and a multi-link piston crank mechanism. The multi-link piston crank mechanism controls movement of the piston such that an acceleration of the piston at top dead center is less than an acceleration of the piston at bottom dead center. A determining device determines an operating condition of the engine. A combustion mode control device controls the engine to operate at an air-fuel ratio leaner than a stoichiometric air-fuel ratio when the determining device determines that the operating condition of the engine is in a predetermined operating region.