An air-fuel ratio control controls an air-fuel ratio (air-fuel ratio of an engine) of a mixture supplied to the engine, based on an output value of the downstream-side air-fuel ratio sensor disposed downstream of a catalyst. That is, the air-fuel ratio control apparatus sets the air-fuel ratio of the engine at a rich air-fuel ratio when the output Voxs is smaller than a reference value VREF (when a rich request is occurring). The air-fuel ratio control apparatus sets the air-fuel ratio of the engine at a lean air-fuel ratio when the output Voxs is larger than a reference value VREF (when a lean request is occurring). The air-fuel ratio control apparatus makes the target value VREF gradually come closer to a reference value VF (stoichiometric air-fuel ratio corresponding value) from a certain value, when the output value Voxs deviates greatly from the reference value Vf (points P1-P3).