Active air-fuel ratio control is performed to alternately control an air-fuel ratio in an area located upstream of a catalyst between a lean side and a rich side. Switching is carried out between lean control and rich control at the same time when an output from a post-catalyst sensor reaches a threshold. Whether the catalyst is normal or abnormal is determined based on the rate of a change in the output from the post-catalyst sensor between a first point of time when a pre-catalyst air-fuel ratio reaches stoichiometry after the output from the post-catalyst sensor reaches the threshold and a second point of time when the output from the post-catalyst sensor reaches the threshold next time.