A determination oxygen storage amount used to determine whether a catalyst is degraded is a value obtained by applying a correction amount for removing error caused by response delay time of an output signal of an oxygen sensor to an oxygen storage amount calculated every short time. The correction amount is a value that is calculated using slopes stored in memory, i.e., the slopes for the number of storage cycles (>the short time) corresponding to the response delay time, or the like, and becomes more accurate as a value corresponding to the error as the storage cycle becomes relatively shorter with respect to the response delay time and the number of the slopes stored in the memory increases. The necessary storage capacity of the memory is inhibited from increasing excessively even if the number of the slopes stored in the memory is large.