An electrically driven power steering apparatus develops an assisting steering force to be applied to a steering system in accordance with a driving force detected, by detecting a driving force which is applied to a steering system from steering means and allowing an electric motor of an electric drive mechanism to be energized at a higher power level when the driving force detected is of an increased magnitude and at a reduced power level when the detected driving force is of a reduced magnitude. A voltage output from an onboard power supply is monitored, and when the voltage is below a given value, the motor is energized at a power level which is less than the energization power level which corresponds to the detected driving force. In this manner, a degradation of the onboard battery is prevented which would result from the operation of the electrically driven power steering apparatus when the battery voltage is low or when the charging power is insufficient. The energizing power level applied to the motor is limited by two alternative methods. In one method, the energization of the motor above an upper limit of energization power level is inhibited. In a second method, a lower limit is established for a response driving force, and the energization of the motor is inhibited in response to a driving force which is below the lower limit.