An electric power steering apparatus comprising: an electric motor that generates a steering assist force; a motor control device that drives and controls the electric motor based on a target current value; a steering torque detector that detects steering torque; a basic assist current value setting device that sets a basic assist current value by using the steering torque that is detected by the steering torque detector; a relative steering angle detector that detects a relative steering angle; a neutral position determining device that determines a steering neutral position by detecting a straight traveling state of a vehicle; an absolute steering angle computation device that computes an absolute steering angle serving as an absolute steering angle with respect to the steering neutral position determined by the neutral position determining device, based on the relative steering angle that is detected by the relative steering angle detector; a compensating current value computation device (61, 73) that computes a compensating current value for steering wheel return control of applying torque in such a direction that a steering wheel returns to a neutral position when a driver returns the steering wheel to the neutral position, by using the absolute steering angle that is computed by the absolute steering angle computation device; a basic assist current value correction device (54, 55, 42) that changes the basic assist current value that is set by the basic assist current value setting device, according to whether it is before or after the absolute steering angle computation device is allowed to compute the absolute steering angle; and a target current value computation device that computes the target current value by using the basic assist current value corrected by the basic assist current value correction device and the compensating current value computed by the compensating current value computation device, characterized in that, on the condition that the neutral position determining device determines that the vehicle is in the straight traveling state, the basic assist current value correction device decreases an absolute value of the basic assist current value that is set by the basic assist current value setting device, before the absolute steering angle computation device is allowed to compute the absolute steering angle. an electric motor that generates a steering assist force; a motor control device that drives and controls the electric motor based on a target current value; a steering torque detector that detects steering torque; a basic assist current value setting device that sets a basic assist current value by using the steering torque that is detected by the steering torque detector; a relative steering angle detector that detects a relative steering angle; a neutral position determining device that determines a steering neutral position by detecting a straight traveling state of a vehicle; an absolute steering angle computation device that computes an absolute steering angle serving as an absolute steering angle with respect to the steering neutral position determined by the neutral position determining device, based on the relative steering angle that is detected by the relative steering angle detector; a compensating current value computation device (61, 73) that computes a compensating current value for steering wheel return control of applying torque in such a direction that a steering wheel returns to a neutral position when a driver returns the steering wheel to the neutral position, by using the absolute steering angle that is computed by the absolute steering angle computation device; a basic assist current value correction device (54, 55, 42) that changes the basic assist current value that is set by the basic assist current value setting device, according to whether it is before or after the absolute steering angle computation device is allowed to compute the absolute steering angle; and a target current value computation device that computes the target current value by using the basic assist current value corrected by the basic assist current value correction device and the compensating current value computed by the compensating current value computation device, the basic assist current value correction device decreases an absolute value of the basic assist current value that is set by the basic assist current value setting device, before the absolute steering angle computation device is allowed to compute the absolute steering angle.