[Problem]The present invention provides a motor control apparatus that is capable of making the whole system robust not only with respect to motor parameter variations such as the temperature variation and the manufacturing unevenness but also with respect to disturbances and an electric power steering apparatus mounting the motor control apparatus thereon.[Means for solving the problem]The motor control apparatus comprises a current detector for detecting a current of a motor and a controller for deciding a voltage command value based on at least a current command value, the controller comprises an adaptive identifying means for identifying parameter variations of an output model of the motor, a current estimating means for estimating a current of the motor, and a voltage command value deciding means for deciding the voltage command value, and the adaptive identifying means performs the identification based on at least a current detection value detected by the current detector and a current-estimate value calculated by the current estimating means, the current estimating means calculates the current-estimate value based on at least a result of the identification and the voltage command value, the voltage command value deciding means decides the voltage command value based on the current command value and the current-estimate value.