When an accelerator opening degree becomes zero, a fuel cut-permission vehicle speed is set on the bases of a cooling water temperature. During a delay time, torque reduction has the characteristic of being dependent on cooling water temperature, and in an unwarmed state, a relatively large amount of air is supplied. The fuel cut-permission vehicle speed has the characteristic of taking a high value when an engine is not warmed up and cooling water temperature is low, in accordance with delay time air amount reduction control, which is performed in accordance with cooling water temperature. This reduces any shocks or odd feelings experienced by an occupant.