During a learning mode period, the fuel correction coefficient is forcibly changed three times from a situation in which no correction is necessary, whereby the fuel injection quantity of each cylinder is forcibly changed three times. A cross-correlation between the estimated air-fuel ratio and the fuel correction coefficient, which are calculated based on the detected value of the air-fuel ratio sensor every 60.degree. CA, is evaluated to learn a deviation of the air-fuel ratio detecting timing from the appropriate value.