A NOx catalyst is provided on an exhaust passage of an engine. The NOx catalyst reduces the occluded NOx when an air-fuel ratio of exhaust gas is in the vicinity of a stoichiometric air-fuel ratio or in a richer state than the stoichiometric air-fuel ratio. Turbocharging is executed by turbochargers. In a low load region within the reduction execution region, a target air-fuel ratio is achieved, as required for NOx reduction, by air amount adjustment with an air amount control valve provided on an intake passage. Since a large amount of air is needed in the high load region within the reduction execution region, the target air-fuel ratio is achieved by air amount adjustment using turbocharging pressure control.