A control apparatus of an electric power steering apparatus is provided in which a nonlinear element of a motor model of-the electric power steering apparatus is compensated beforehand to linearize the motor model and the back electromotive force of the motor is computed to compensate the back electromotive force for a control loop, and conduct back electromotive force compensation with no lag in order to realize a control apparatus of an electric power steering apparatus with less control error, stable controllability, small motor output torque ripple, good wheel steering feeling, and less motor noise.