To exhibit purifying performance having an exhaust purifying catalyst to the maximum extent by amplifying a target air-fuel ratio at a predetermined period for a predetermined amount, in a device formed in such a constitution that an air-fuel ratio of engine intake mixture to the target air-fuel ratio on the basis of a result detected by a wide region air-fuel ratio.

During traveling of a vehicle, it is judged whether a wide region air-fuel ratio sensor 18 and a downstream oxygen sensor 19 are activated in a control unit 50 or not. When it is activated, it is judged whether an air-fuel ratio feed back control condition is materialized or not. When it is 'YES', it is judged whether an allowable condition of perturbation control is materialized or not. When the judgment is 'YES', an air fuel ratio of engine intake mixture is controlled to an after correction target air-fuel ratio which is set by a target air-fuel ratio correcting means on the basis of a result detected by the wide region air-fuel ratio sensor 18, and also the after correction target air-fuel ratio is controlled so as to amplify at a predetermined cycle for a predetermined rate. It is thus possible to adsorb or release oxygen molecule on a surface of a catalytic converter rhodium 20 effectively.