The engine disclosed features an engine cylinder provided with an air intake valve, an injector having a fuel injection port which is directed towards an interior of the engine cylinder, and a control unit which is connected to the air intake valve and to the injector, the control unit effecting changes in the air intake amount by controlling the degree of opening of the air intake valve, and, also, controls the air/fuel ratio by changing the amount of fuel supplied by the injector. The engine also has an exhaust valve in the engine cylinder such that the control unit controls the intake valve and the exhaust valve so that an opening period of the intake valve is overlapped with an opening period of the exhaust valve at least when the opening period of the intake valve is maximum. The period of the overlap is longer when a relatively large amount of air is required than when a relatively small amount of air is required. According to such a scheme, the amount of the air can be changed by the lift of the intake valve. By changing the lift, the overlap with an exhaust valve is also changed. During the high-output or power operation, the period of overlap between the exhaust valve and the intake valve is made longer. When engine torque decreases to a level lower than the target engine torque, the air amount is adjusted by the cam or the throttle valve.