An apparatus for determining an air-fuel ratio imbalance among cylinders based on an output value of an air-fuel ratio sensor, an imbalance determination parameter which becomes larger or smaller as a difference among air-fuel ratios becomes larger, and performs determining an air-fuel ratio imbalance among cylinders based on a result of a comparison between the imbalance determination parameter and a imbalance determination threshold. The determining apparatus calculates a purge correction coefficient which compensates for a change in the air-fuel ratio due to an evaporated fuel gas which is generated in a fuel tank, while the evaporated fuel gas is being introduced into an intake passage, and corrects a fuel injection amount with the purge correction coefficient FPG.