When two abnormal cylinders are causing variation abnormality, these abnormal cylinders are identified. A parameter correlated with a degree of fluctuation of output from an air-fuel ratio sensor installed in an exhaust passage common to a plurality of cylinders is calculated. Based on the calculated parameter, inter-cylinder air-fuel ratio variation abnormality is detected. The following steps are carried out: (A) a step of forcibly changing amounts of fuel injected for two of the plurality of cylinders and calculating the parameter, (B) a step of changing the two cylinders to other two cylinders and repeating the step (A), and (C) a step of identifying two cylinders causing variation abnormality based on a plurality of the parameters calculated in the steps (A) and (B).