In an electric power steering apparatus which comprises a motor for generating steering assist force, it is judged whether or not the vehicle is in a state of straight forward motion. A mean reference steering angle is determined by dividing total of relative steering angles which are determined when the vehicle is judged to be in a state of straight forward motion by the number of judgments that the vehicle is in a state of straight forward motion. A steering angle is determined by subtracting a steering angle midpoint from a relative steering angle with taking the mean reference steering angle as the steering angle midpoint. The output of the motor for generating steering assist force is corrected in accordance with an output correction value determined on the basis of the determined steering angle. This output correction value is altered so as to have a positive correlation with the number of judgments that the vehicle is in a state of straight forward motion.