To improve convergent responsiveness to a target air-fuel ratio, in a device to calculate a linear item and an integrated non-linear item through control of a sliding mode and perform feedback control of an air-fuel ratio.

A non-linear item UNL is calculated as UNL=(a gain 1)×(a target air-fuel ratio - an actual air-fuel ratio)/(a target air-fuel ratio - an actual air-fuel ratio)+UNL(OLD). A linear item UL is calculated as UL=(a gain 2)×(a target air-fuel ratio - an actual air-fuel ratio)/an actual fuel ratio, and feedback control of the air-fuel ratio is effected by the addition value. In this case, a value of the non-linear item UNL when an air-fuel ratio is caused to converge to the vicinity of the target air-fuel ratio is learnt classified by the target air- fuel ratio. The non-linear item UNL is initialized to a value learnt corresponding to the target air-fuel ratio after switching.