In an internal combustion engine in which air-fuel ratio feedback control is performed using an A/F sensor mounted upstream of an exhaust gas purifying catalyst, a deviation in the characteristic of the A/F sensor is estimated and the air-fuel ratio feedback control and catalyst deterioration judging processes are performed accounting for the estimated deviation. If the characteristic of the A/F sensor deviates in an output increasing direction, the amount of fuel correction will become excessively large, and the period from the time an output voltage VAF crosses a target voltage VAFT to the time it returns to the target voltage will become short compared with a normally functioning A/F sensor. On the other hand, if the characteristic of the A/F sensor deviates in an output decreasing direction, the amount of fuel correction will become excessively small, and that period will become long compared with a normally functioning A/F sensor. In the present invention, the output voltage VAF of the A/F sensor is monitored, and its amplitude VP and period CPER are calculated; then, based on the relationship between them, a correction factor K for correcting VAF based on the characteristic deviation is obtained. Instead of the amplitude VP and period CPER, a response curve length and an area enclosed by VAF and VAFT may be used.