A compensation control apparatus of motor driven power steering (MDPS) may include: a torque sensor for measuring a driver's column torque inputted to a steering wheel; and a controller for generating an assist torque based on the column torque measured through the torque sensor, compensating for a phase margin in a low-frequency band for the generated assist torque, detecting a resonance frequency to attenuate resonance, and outputting a final assist torque. According to the invention, when the assist torque is determined based on the boost output of vehicle speed and torque of pipe column on the MDPS system, reduction and delay of the responsiveness of low frequency band caused by effects on a stabilization filter are compensated via an advance filter and a stabilization filter which are mutually cascaded.