The present invention provides an air-fuel ratio feedback control apparatus for an internal-combustion engine. The apparatus includes an air-fuel ratio detector that is disposed in an exhaust system of the engine so as to detect an air-fuel ratio of exhaust gas, NOx purifier for purifying NOx contained in the exhaust gas during a lean operation and feedback controller for making a feedback control upon an air-fuel ratio of air-fuel mixture to be supplied to the engine based on an output of the air-fuel ratio detector. A diagnostic system diagnoses the NOx purifier based on an output of an O2 sensor disposed downstream of the NOx purifier when the air-fuel ratio of the air-fuel mixture to be supplied to the engine has been changed from lean to rich and gain changer for making a feedback control gain of the feedback controller smaller when the air-fuel ratio is changed from lean to rich.