A control apparatus includes a driving device that is capable of operating regardless whether the engine is running or not. A variable valve actuation mechanism is driven by the driving device. During an idling operation of the engine, a control section controls the driving device such that the variable valve actuation mechanism maintains the valve timing at a valve timing advanced relative to a most retarded valve timing. The control section controls the driving device such that the variable valve actuation mechanism changes the valve timing to the most retarded valve timing after a stopping operation of an autonomous operation of the engine is initiated. Therefore, shock due to the initiation of the engine starting operation is reduced without decreasing fuel economy.