In an engine exhaust system, an NOx catalyst for occluding NOx in a state of the lean air-fuel ratio and reducing the occluded NOx in the state of the rich air-fuel ration A CPU sets a target air-fuel ratio of a mixture supplied to an engine to the lean side with respect to the stoichiometric air-fuel ratio for the lean mixture combustion. The CPU sets a rich time for a rich mixture combustion in accordance with the engine operating state and the NOx purification rate in the NOx catalyst. In this moment, the shortest rich time is set within a range in which a desired NOx purification rate by the NOx catalyst is obtained. A three-way catalyst may be arranged upstream of the NOx catalyst. The three-way catalyst carries only a noble metal such as platinum having no oxygen storing capability.