An NOx-absorbing and reducing catalyst device (7) is disposed in an exhaust passage of an engine (1). The NOx concentration in exhaust gas flowing out of the catalyst device is detected by an NOx sensor (33). Every time the NOx concentration detected by the NOx sensor increases to a predetermined value, an electronic control unit (ECU) (30) of the engine reactivates the NOx-absorbing and reducing catalyst device (7) by operating the engine (1) at a rich air fuel ratio for a short time. The ECU (30) also detects a deviation of the output of the NOx sensor (33) on the basis of a reference value (corresponding to zero NOx concentration) and an output of the NOx sensor (33) produced when the engine is being operated in a condition where the amount of NOx discharged from the engine is small, for example, a condition where the air-fuel ratio is on the lean side and the load is low (that is, in a condition where the NOx concentration in exhaust gas reaching the NOx sensor (33) becomes substantially zero). Based on the detected deviation, the ECU (30) corrects the output of the NOx sensor (33).