In an exhaust path of an internal combustion engine, a catalyst, a first air-fuel ratio sensor installed upstream thereof, and a second air-fuel ratio sensor installed downstream thereof are disposed. An air-fuel ratio of the engine is controlled to a rich air-fuel ratio or a lean air-fuel ratio. In a state that is determined as a state where the catalyst stores oxygen to an upper limit after the air-fuel ratio is switched to the lean air-fuel ratio from the rich air-fuel ratio, or a state where the catalyst releases oxygen to a lower limit after the air-fuel ratio is switched to the rich air-fuel ratio from the lean air-fuel ratio, a first output from the first air-fuel ratio sensor, and a second output from the second air-fuel ratio sensor are detected and based on a difference therebetween the output of the first air-fuel ratio sensor is corrected.