To prevent the occurrence of errors when fuel control is returned to air-fuel ratio control wherein a catalyst oxygen retention volume after fuel cut is kept in the maximum effective oxygen retention volume.

Catalyst 21 disposed to an exhaust passage holds an oxygen retention capacity. When an air-fuel ratio in exhaust gas at the downstream of the aforesaid catalyst is changed from a stoichiometric condition to a lean condition, the oxygen retention volume of the catalyst at that time is stored in a memory means 22 as the maximum effective oxygen retention volume, when an air-fuel ratio in exhaust gas at the downstream of the catalyst is found to be close to a stoichiometric condition, a value estimating an under and over oxygen volume flowing over the catalyst per specified hour, is operated as a catalyst oxygen retention volume by an operating means 23. When a specified air-fuel ratio condition is not satisfied, and when the aforesaid air-fuel ratio is lean, a late reaction oxygen absorbing volume per specified hour, by which oxygen is slowly absorbed by the catalyst, is estimated so as to allow a catalyst oxygen retention volume exceeding the maximum effective oxygen retention volume to be operated by an operating means 24. And when a specified air-fuel ratio condition is satisfied, an air-fuel ratio shall be controlled by a control means 25 so as to allow a catalyst oxygen retention volume at that time to be within the maximum effective retention volume.