An electric power steering apparatus that has an assist mode which controls a motor applying an assist torque to a steering system of a vehicle when steering said steering system and an automatic mode which controls said motor depending on a target steering angle supplied from said vehicle as needed when said vehicle autonomously runs, comprising: a torque control section to calculate a first motor current command value based on a vehicle speed of said vehicle and a steering torque inputted into a steering shaft of said steering system; a steering angle control section to calculate a second motor current command value based on said target steering angle, an actual steering angle and a motor angular velocity of said motor; and a vehicle motion control section to calculate said target steering angle based on vehicle information, characterized in that said vehicle motion control section comprises: a rate limiter whose output value is coincident with a lateral position command by changing said output value in a step form with reference to said lateral position command in a predetermined period; a lateral position command vibration removing section to remove vibration frequency components of an output of said rate limiter; a lateral velocity calculating section to calculate a lateral velocity based on a lateral position; a lateral position control section to input a difference between said lateral position and an output value of said lateral position command vibration removing section, and to output a lateral velocity command value; a lateral velocity control section that comprises an integration section to integrate a deviation between said lateral velocity command value and said lateral velocity; and a proportion section to input said lateral velocity, and outputs a subtracted value by subtracting an output of said proportion section from an output of said integration section; and a vehicle behavior stabilizing section to input a yaw rate signal and to pass said yaw rate signal whose frequency having a predetermined cut-off frequency or more, wherein said vehicle motion control section adds an output of said vehicle behavior stabilizing section to an output of said lateral velocity control section, and sets as said target steering angle. a torque control section to calculate a first motor current command value based on a vehicle speed of said vehicle and a steering torque inputted into a steering shaft of said steering system; a steering angle control section to calculate a second motor current command value based on said target steering angle, an actual steering angle and a motor angular velocity of said motor; and a vehicle motion control section to calculate said target steering angle based on vehicle information, characterized in that said vehicle motion control section comprises: a rate limiter whose output value is coincident with a lateral position command by changing said output value in a step form with reference to said lateral position command in a predetermined period; a lateral position command vibration removing section to remove vibration frequency components of an output of said rate limiter; a lateral velocity calculating section to calculate a lateral velocity based on a lateral position; a lateral position control section to input a difference between said lateral position and an output value of said lateral position command vibration removing section, and to output a lateral velocity command value; a lateral velocity control section that comprises an integration section to integrate a deviation between said lateral velocity command value and said lateral velocity; and a proportion section to input said lateral velocity, and outputs a subtracted value by subtracting an output of said proportion section from an output of said integration section; and a vehicle behavior stabilizing section to input a yaw rate signal and to pass said yaw rate signal whose frequency having a predetermined cut-off frequency or more, a rate limiter whose output value is coincident with a lateral position command by changing said output value in a step form with reference to said lateral position command in a predetermined period; a lateral position command vibration removing section to remove vibration frequency components of an output of said rate limiter; a lateral velocity calculating section to calculate a lateral velocity based on a lateral position; a lateral position control section to input a difference between said lateral position and an output value of said lateral position command vibration removing section, and to output a lateral velocity command value; a lateral velocity control section that comprises an integration section to integrate a deviation between said lateral velocity command value and said lateral velocity; and a proportion section to input said lateral velocity, and outputs a subtracted value by subtracting an output of said proportion section from an output of said integration section; and a vehicle behavior stabilizing section to input a yaw rate signal and to pass said yaw rate signal whose frequency having a predetermined cut-off frequency or more, wherein said vehicle motion control section adds an output of said vehicle behavior stabilizing section to an output of said lateral velocity control section, and sets as said target steering angle.