An electrically driven power steering system for a vehicle comprises a steering sensor for detecting a steering operation of a steering wheel and a power steering control unit, which receives a command signal from a vehicle movement total control unit, calculates a target steering assist torque from a steering signal from the steering sensor and the command signal and drives a steering assist electric motor in accordance with the above calculated target steering assist torque. The power steering control unit further calculates a feasible torque to be generated at the steering assist electric motor, and drives the steering assist electric motor at the feasible torque, when the feasible torque is lower than the target steering assist torque, namely when a driving current to the electric motor should be limited due to an increased temperature of the electric motor and so on.