A drive system for an electrically driven dump truck is capable of enabling electric motors for traveling to make full use of the output horsepower of the prime mover up to an output limit of the prime mover. A target motor horsepower corresponding to an operation amount of an accelerator pedal is calculated and an available maximum horsepower for the electric motors out of the maximum output horsepower of the prime mover is calculated in response to the actual revolution speed of the prime mover. The horsepower coefficient corresponding to the instantaneous revolution speed deviation is calculated. The available maximum horsepower for the electric motors is modified by the horsepower coefficient to determine a second target motor horsepower. The target motor horsepower is limited to not exceed the second target motor horsepower so as to control the torque of the electric motors.