A SOx trap catalyst, an oxidation catalyst, a particulate filter, an aqueous urea supply valve, and a NOx selective reduction catalyst are arranged in order from upstream to downstream in an engine exhaust passage. It is determined whether a discharge concentration of hydrogen sulfide H2S will become equal to or greater than a preset maximum concentration when SOx is released from the SOx trap catalyst. If it is estimated that the discharge concentration of the hydrogen sulfide H2S will become equal to or greater than the maximum concentration when SOx is released, an adsorbed ammonia amount adsorbed on the NOx selective reduction catalyst is reduced before SOx is released so that the discharge concentration of the hydrogen sulfide H2S is less than the maximum concentration when SOx is released.