An electronic power steering apparatus for a vehicle having a steering mechanism to generate a steering assisting force includes: a steering angle sensor; a steering torque sensor; a target steering torque setting unit for setting a target steering torque based on the detected steering angle; a torque deviation computing unit for computing a torque deviation between the target steering torque and the detected steering torque; a first target current value computing unit for computing a first target current value for generating a steering assisting force by the motor based on the computed torque deviation; and a vehicle speed sensitivity adjusting unit that adjusts the first target current value, at least corresponding to a detected vehicle speed, and outputs the adjusted first current value as a second target current value. The motor control unit controls the motor to generate the steering assisting force based on the second target current value.