When a vehicle speed V is greater than a threshold value Vref when an engine speed difference ΔN between an engine speed Ne and a target engine speed Ne* is greater than a threshold value Nref and a catalyst degradation flag Fc is 1, that engine speed Ne is brought to the target engine speed Ne* while the engine is kept firing. However, when the vehicle speed V is less than the threshold value Vref, a fuel cut is executed even if the engine speed difference ΔN is greater than the threshold value Nref and the catalyst degradation flag Fc is 1. The threshold value Vref is set based on a catalyst bed temperature CT so control to suppress catalyst degradation can be continued for longer the more the operating state is such that the catalyst bed temperature CT is high and degradation of the catalyst is promoted.