An engine includes variable valve mechanisms and a variable compression ratio mechanism. An ECU executes temperature balance control when a fuel-cut operation is executed. In the temperature balance control, valve opening characteristics of an exhaust valve are controlled based on a magnitude relation between an actual catalyst temperature and a target catalyst temperature and a magnitude relation between a water temperature and a required cylinder wall temperature. When executing a fuel-cut operation, it is thereby possible to control both the actual catalyst temperature and the water temperature in a well-balanced manner so that the actual catalyst temperature falls within a temperature range suitable for operation of the catalysts, and the water temperature becomes close to the required cylinder wall temperature.