An inter-cylinder air-fuel-ratio imbalance determination apparatus includes an air-fuel-ratio sensor in an exhaust passage of an engine. The air-fuel-ratio sensor functions as a limiting-current-type wide range air-fuel-ratio sensor when a voltage is applied, and functions as a concentration-cell-type oxygen concentration sensor when no voltage is applied. The determination apparatus causes the air-fuel-ratio sensor to function as the limiting-current-type wide range air-fuel-ratio sensor, and executes air-fuel ratio feedback control on the basis of the output value of the air-fuel-ratio sensor. When an imbalance determination parameter is obtained, the determination apparatus causes the air-fuel-ratio sensor to function as the concentration-cell-type oxygen concentration sensor, and obtains, as the imbalance determination parameter, a value corresponding to the differentiated value of the output value of the air-fuel-ratio sensor. The determination apparatus determines an inter-cylinder air-fuel-ratio imbalance state, when the absolute value of the imbalance determination parameter is greater than an imbalance determination threshold value.