a catalyst that is disposed in the exhaust system and has an oxygen occlusion function and an oxidation function for purifying exhaust gases;

a NOx catalyst that is disposed in the exhaust system at a location downstream of the catalyst, for trapping NOx contained in exhaust gases in an oxidizing atmosphere, and reducing the trapped NOx in a reducing atmosphere to thereby purify the trapped NOx;

NOx reduction control means for executing reduction control in which the exhaust gases flowing into said NOx catalyst are controlled to the reducing atmosphere, by supplying reducing agent to an upstream side of said catalyst so as to cause said NOx catalyst to carry out an operation for reducing NOx;

oxygen occlusion amount-calculating means for calculating an amount of oxygen occluded in said catalyst as an oxygen occlusion amount;

reducing agent consumption amount-calculating means for calculating an amount of reducing agent consumed by oxidation in said catalyst during execution of the reduction control by the NOx reduction control by said NOx reduction control means, as a reducing agent consumption amount, according to the calculated oxygen occlusion amount;

reducing agent supply amount-calculating means for calculating an amount of reducing agent supplied to said NOx catalyst, as a reducing agent supply amount, according to the calculated reducing agent consumption amount; and

reduction control-terminating means for terminating the reduction control when the calculated reducing agent supply amount exceeds a threshold value.