An air-fuel ratio imbalance determining apparatus that is configured to sequentially stop a fuel injection for each of cylinders in accordance with a firing (ignition) order by changing the intake valves and exhaust valves of the cylinder whose fuel injection is stopped from a valve operating state to a valve resting state. After a predetermined time elapses (time-point tp), an upstream-side air-fuel ratio value obtained based on an output value of an upstream air-fuel ratio sensor disposed in the exhaust passage which becomes a value corresponding to an air-fuel ratio of the final gas. The determining apparatus obtains that value as data relating to an air-fuel ratio of the cylinder which discharged the final gas, and determines whether or not an air-fuel ratio imbalance is occurring based on the data relating to the air-fuel ratio of each of the cylinders.