To extend a rich time for S poisoning recovery control at a proper timing utilizing that the degree of a front end S poisoning degradation which is the degradation of an NOx catalyst due to the deposition of sulfur components is large at the exhaust front end of the NOx catalyst.

The degree of the front end S poisoning degradation of the NOx catalyst is larger as the total S inflow amount SU which is the total amount of the sulfur components flowing into the NOx catalyst from the start of use of an internal combustion engine is larger. With this taken into consideration, the degree of the degradation is estimated based on the total S inflow amount SU. Specifically, the degree of the degradation is estimated based on the total inflow amount SU referring to a map in which the relation between the total inflow amount SU obtained by experiments beforehand and the degree of the degradation is specified. Consequently, the estimated degree of the degradation becomes accurate, and the rich time for the S poisoning recovery control is extended at a proper timing based on the degree of the degradation.