A selective reduction catalyst is disposed in an exhaust passage of an engine for reducing NOx in exhaust gases from the engine under existence of a reducing agent. The reducing agent or a reactant for generating the reducing agent is supplied to the upstream side of the selective reduction catalyst. Occurrence of a reducing-agent slip in which the reducing agent is discharged to the downstream side of the selective reduction catalyst is determined. A storage amount indicative of an amount of the reducing agent stored in the selective reduction catalyst is temporarily reduced from the state where the storage amount is at the maximum, and thereafter the storage amount is increased until the occurrence of the reducing-agent slip is detected. A supply correction amount for correcting an amount of the reducing agent is calculated according to an occurrence state of the reducing agent slip when the storage amount is changed.