An inter-cylinder air-fuel ratio imbalance determination apparatus that obtains, based on an output value Vabyfs of an air-fuel ratio sensor, an air-fuel ratio fluctuation indicating amount (AFD) which becomes larger as an air-fuel ratio fluctuation of an exhaust gas passing through a position at which the air-fuel ratio sensor is disposed becomes larger, during a parameter obtaining period. The determination apparatus estimates an air-fuel ratio sensor element temperature (Temps) having a strong relation with responsiveness of the air-fuel ratio sensor during the parameter obtaining period, and obtains a corrected air-fuel ratio fluctuation indicating amount by correcting the AFD based on the estimated Temps. The determination apparatus adopts the corrected air-fuel ratio fluctuation indicating amount as the imbalance determination parameter X, and determines whether or not an inter-cylinder air-fuel-ratio imbalance state has been occurring based on a comparison between the imbalance determination parameter X and the imbalance determination threshold Xth.