When executing a Local-learning, an air-fuel ratio detecting time is corrected so that a dispersion of detection values of an air-fuel ratio sensor becomes a maximum value in one cycle of an engine. While executing a cylinder-by-cylinder air-fuel ratio control, a Global-learning is executed. In the Global-learning, the air-fuel ratio detecting time is corrected based on a relationship between a variation in estimated air fuel ratio of each cylinder and a variation in fuel quantity correction value of each cylinder. In the Global-learning, a computer computes a correlation coefficient between the variation in estimated air-fuel ratio and the variation in fuel quantity correction value of the cylinder for each case where the cylinder assumed to correspond to the estimated air fuel ratio is hypothetically varied in multiple ways. Then, the air-fuel ratio detecting time is corrected so that this correlation coefficient becomes a maximum value.