An air-fuel ratio feedback control of an internal combustion engine is performed, by a sliding mode control, by computing an air-fuel ratio feedback control amount including a linear term and a nonlinear term, and at the time of when switching a target air-fuel ratio or at the time of when switching the operating condition, such as the cutting of purge, where the air-fuel ratio is changed, the nonlinear term is initializing to a predetermined value corresponding to the post-switched operating condition.