To accurately diagnose deterioration of a catalyst by a simple and convenient composition.

When fuel injection is restarted (S2) from a state of a maximum quantity of oxygen adsorbed in a catalyst by a fuel cut (S1), an oxygen deficient state is provided by incrementally correcting a fuel injection quantity (S3) so that the adsorbed oxygen is consumed. When a predetermined time has passed from a fuel injection restart (S4) and an air-fuel ratio sensor provided in a downstream side of the catalyst detects a rich air-fuel ratio (S5 and S6), it is determined that the oxygen quantity adsorbed by the catalyst in a fuel cut state is low and it is determined that deterioration accompanying reduction of a maximum absorbing oxygen quantity has occurred (S8).