An embodiment (control apparatus) of an air-fuel ratio control apparatus according to the present invention determines, based on an output value Voxs of a downstream air-fuel ratio sensor 56 disposed at a position downstream of a three-way catalyst 43, which air-fuel request is occurring, a rich request or a lean request. The control apparatus sets an air-fuel ratio of each cylinder (cylinder-by-cylinder air-fuel ratio) to a rich air-fuel ratio when the rich request is occurring, and sets the cylinder-by-cylinder air-fuel ratio to a lean air-fuel ratio when the lean request is occurring. The control apparatus has a cylinder-by-cylinder air-fuel ratio of a specific cylinder different from a cylinder-by-cylinder air-fuel ratio of the other cylinder so as to obtain a fluctuation period correlated value indicative of a fluctuation of the output value Voxs of the downstream air-fuel ratio sensor 56, and determines an influence/impact degree on the output value of the downstream air-fuel ratio sensor of an exhaust gas discharged from each of a plurality of cylinders, based on the fluctuation period correlated value. Further, the control apparatus controls the air-fuel ratio of each cylinder in accordance with the influence degree.