To stably and accurately determine whether or not an inter-cylinder imbalance state in air-fuel ratio has occurred regardless of responsiveness of an air-fuel ratio sensor.

It is assumed that an air-fuel ratio of a mixed exhaust gas passing through a collecting exhaust passage coincides with a target air-fuel ratio (a theoretical air-fuel ratio) through feedback control based on a detected air-fuel ratio from an air-fuel ratio sensor arranged in the collecting exhaust passage in which exhaust passages extending from a plurality of cylinders are collected. When taking as "a unit combustion cycle period" a period in which a crank angle passes and requiring for completing one combustion stroke by each of the plurality of cylinders, an imbalance state is determined to have occurred based on the detection of "a condition in which there exists only one minimal value of a detected air-fuel ratio having a value richer than the target air-fuel ratio in the unit combustion cycle period" or "a condition in which there exists only one maximal value of a detected air-fuel ratio having a value leaner than the target air-fuel ratio in the unit combustion cycle period".