An NOX occluding and reducing catalyst 7 is arranged in an exhaust gas passage 2 of an engine 1 so as to occlude, reduce and purify NOX contained in an exhaust gas. An H2 sensor 33 is arranged in the exhaust gas passage on a downstream side of the NOX occluding and reducing catalyst 7 and a hydrogen component concentration of the exhaust gas is detected. When an amount of NOX occluded in the NOX occluding and reducing catalyst is increased to a predetermined value, an electronic control unit (ECU) 30 of the engine operates the engine at a rich air-fuel ratio, and a regenerating operation, by which a rich air-fuel ratio exhaust gas is supplied to the NOX occluding and reducing catalyst, is executed so as to reduce and purify NOX which is occluded in the NOX occluding and reducing catalyst. At the time of executing the regenerating operation, when the H2 sensor 33 detects hydrogen components in the exhaust gas, ECU 30 finishes the regenerating operation. Due to the foregoing, it is possible to accurately judge the time for terminating the regenerating operation of the NOX occluding and reducing catalyst.