An in-cylinder pressure sensor is provided. It is determined whether a cylinder for which the in-cylinder air-fuel ratio is to be calculated is a rich cylinder or a lean cylinder. A polytropic index in the expansion stroke is calculated from the in-cylinder pressure detected by the in-cylinder pressure sensor. The calculated polytropic index m is corrected based on an operational condition parameter of an internal combustion engine. An in-cylinder air-fuel ratio is calculated based on the corrected polytropic index m in the expansion stroke, the result of the determination of whether the cylinder is a rich cylinder or a lean cylinder, and an m-A/F curve.