An engine includes an intake variable valve mechanism and an exhaust variable valve mechanism. An ECU causes all intake valves in all cylinders to stop in a closed state by means of intake variable valve mechanism when performing a fuel-cut operation, including when the engine is stopped. The ECU causes at least one exhaust valve in all cylinders to stop in an open state by means of exhaust variable valve mechanism. When executing a fuel-cut operation, needless compression can be avoided by stopping the exhaust valves in an open state, while protecting a catalyst from deterioration caused by contact with intake air by stopping the intake valves in a closed state. The amount of oil consumption of the engine, and electric power consumption, vibrations and a tendency for spontaneous ignition to occur at cranking time can be improved.