According to the present invention, provided are an apparatus and a method for controlling a motor of a motor driven power steering system. According to the present invention, the apparatus for controlling a motor of a motor driven power steering system comprises: a steering logic controller calculating and transmitting a current command value to control a motor; a current measurement unit measuring a current applied to the motor; and a control unit calculating a motor position increment value based on the current command value inputted from the steering logic controller, a measurement current value inputted from the current measurement unit, and a pre-stored motor parameter, and driving and controlling the motor by using a current motor position estimated by adding the calculated motor position increment value.
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