A fuel injection amount control system acquires an air-fuel ratio imbalance index value that increases as the degree of ununiformity in the air-fuel ratio among cylinders increases, based on an output value of an upstream air-fuel ratio sensor, and acquires an imbalance index learned value by performing a first-order lag filtering operation for removing noise, on the air-fuel ratio imbalance index value. Also, the fuel injection amount is increased based on the imbalance index learned value. In the filtering operation, the time constant of the filter is set to a smaller value when a magnitude of a difference between the current value and the last value of the air-fuel ratio imbalance index value is equal to or larger than a threshold value.