A purifier equipped with an HC catalyst (14) which not only has the ability to oxidize HC but has the ability to retain HC and release the HC held and for which there are specific conditions under which the amount of HC which is released after holding is larger than the amount of HC which is oxidized. An HC supply control operation in which HC is supplied to the HC catalyst for a specific purpose is performed. When the specific conditions are satisfied in performing the HC supply control operation, then the amount of HC to be supplied to the HC catalyst by the HC supply control operation is reduced or the HC supply control operation is stopped.