A motor-driven power steering apparatus including: a base current calculator configured to calculate a base current, which is a base for a target current, based on a detected torque detected by a torque sensor; a band-pass filter configured to allow a predetermined range of frequency components of the detected torque to the pass through the band-pass filter; a base shimmy compensation current calculator configured to calculate a base shimmy compensation current, considered a base for a shimmy compensation current required to suppress a disturbance torque, based on an extracted torque after passing through the band-pass filter; a shimmy compensation current calculator configured to calculate the shimmy compensation current by correcting the base shimmy compensation current according to magnitude of amplitude of the extracted torque; and a final target current determination unit configured to determine the target current based on the base current and the shimmy compensation current.