When both catalyst degradation and catalyst odor need to be suppressed when a fuel cut condition is satisfied, a fuel cut control is executed giving priority to control for suppressing catalyst odor, though a required air amount G* for idling is drawn in at that time. Therefore, when shifting the engine into an idle state to suppress catalyst degradation after the catalyst odor has been eliminated, the required air amount G* for idling is already being drawn in so there is no need to adjust the air amount. As a result, there is no time delay for air amount adjustment. Therefore, after the control to suppress catalyst odor has ended, a smooth shift can be made into control to suppress degradation of the exhaust gas control catalyst.