By performing main fuel injection and sub fuel injection to perform rich operation of an engine, NOx purging of a NOx catalyst is carried out, and in the NOx purging, the ratio between the main fuel injection quantity and the sub fuel injection quantity is variably determined, within the range of 5:1 to 2:1 where the ratio of the sub fuel injection quantity is relatively great, such that the ratio of the sub fuel injection quantity is greater as the temperature of a three-way catalyst becomes higher.