The occurrence of the misfire having a level at which exhaust purifying function of a catalyst is impaired (OT-level misfire) is detected. Upon the detection of the OT-level misfire, basic OT risk from the misfire is multiplied by a correction coefficient corresponding to the accumulated PM amount on the catalyst. The basic OT risk from the misfire is a basic value of OT risk from the misfire which is set based on the operating condition of the engine. The correction coefficient is set to a smaller value as the accumulated PM amount increases. Therefore, the OT risk from the misfire after the multiplication decreases as the accumulated PM amount increases. When a predetermined judgement condition with the OT risk from the misfire is established, it is judged that the misfire having the level occurs.