An oscillation signal is generated to oscillate the air-fuel ratio with a set frequency which is different from a 0.5th-order frequency (half of the frequency corresponding to a rotational speed of the engine). Air-fuel ratio perturbation control is performed to oscillate the air-fuel ratio according to the oscillation signal. An intensity of the 0.5th-order frequency component and the set frequency component contained in the detected air-fuel ratio signal are calculated. A determination parameter applied to determining an imbalance degree of air-fuel ratios corresponding to the plurality of cylinders is calculated according to the two intensities and determines an imbalance failure that the imbalance degree of the air-fuel ratios exceeds an acceptable limit. A predicted imbalance value, indicative of a predicted value of the imbalance degree, is calculated, and an amplitude of the oscillation signal is set according to the predicted imbalance value.