A deviation amount of a downstream air-fuel ratio sensed with a downstream air-fuel ratio sensor, which senses an air-fuel ratio of exhaust gas downstream of a catalyst, from a target air-fuel ratio is integrated during a period in which the downstream air-fuel ratio continuously shows deviations from the target air-fuel ratio while main feedback control and sub feedback control are performed based on outputs of an upstream air-fuel ratio sensor and the downstream air-fuel ratio sensor respectively. The thus-calculated continuous deviation amount of the downstream air-fuel ratio (deterioration degree of exhaust gas purification rate) is compared with an abnormality determination value to determine existence/nonexistence of an abnormal state where the exhaust gas purification rate is deteriorated by an air-fuel ratio variation among cylinders (i.e., state where control center of main feedback control has shifted).