An inter-cylinder air-fuel ratio imbalance determination apparatus (determination apparatus) according to the present invention obtains, based on the output value of the air-fuel ratio sensor, an imbalance determination parameter 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 energizes the heater of the air-fuel ratio sensor in such a manner that a temperature of the air-fuel ratio element during the parameter obtaining period is higher than a temperature of the air-fuel ratio element during a period other than the parameter obtaining period. Accordingly, the imbalance determination parameter is obtained while the responsiveness of the air-fuel ratio sensor is high, and thus, the inter-cylinder air-fuel-ratio imbalance determination having a high accuracy can be made.