An output signal from a downstream-side exhaust gas sensor is fed back into a fuel injection rate so that the air-fuel ratio of the exhaust gases flowing out from a catalyst may match a reference value. In this sub-feedback control process, the integral value of the deviation between the output signal of the downstream-side exhaust gas sensor and a reference value is calculated, and the resulting integral-data signal is smoothed. A learning value for compensating for the permanent error included in an air-fuel ratio signal from an A/F sensor is learnt from the integral-data signal generated by the above smoothing operation.