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.

An internal combustion engine includes a three-way catalyst provided in an exhaust path, an upstream-side air-fuel ratio sensor provided on the exhaust upstream side of the three-way catalyst, and a downstream-side air-fuel ratio sensor provided on the exhaust downstream side of the three-way catalyst. The CPU executes a correction process of making a correction of addressing an output deviation of the upstream-side air-fuel ratio sensor based on an output of the upstream-side air-fuel ratio sensor and an output of the downstream-side air-fuel ratio sensor in a case where the output of the downstream-side air-fuel ratio sensor indicates a value near the stoichiometric air-fuel ratio during the execution of air-fuel ratio control of controlling the air-fuel ratio of an air-fuel mixture based on the output of the upstream-side air-fuel ratio sensor such that the air-fuel ratio of the air-fuel mixture is an air-fuel ratio near the stoichiometric air-fuel ratio.