The oxygen storage capacity preceding a previous oxygen storage capacity and the previous oxygen storage capacity of each of an upstream catalyst and a downstream catalyst are measured, and a present oxygen storage capacity of the downstream catalyst is measured. Then, sulfur poisoning of the upstream catalyst and the downstream catalyst is detected on the basis of an oxygen storage capacity change amount of each of the upstream catalyst and the downstream catalyst from the oxygen storage capacity preceding the previous one to the previous oxygen storage capacity, and the oxygen storage capacity change amount of the downstream catalyst from the previous oxygen storage capacity to the present oxygen storage capacity. The presence/absence of the sulfur poisoning can be accurately detected by utilizing the difference between the manners of sulfur poisoning of the two catalysts.