In this paper, We are proposed a design method of the digital PID controller based on the model following method which minimized the error integral of the step response between the control system and the reference model. And we are applied it by a speed control of the current type inverter induction motor. The dynamic characteristic of the system was expressed by the step response, and then the optimal parameter of the PID controller can be easily obtained by the matrix computation. The derived algorithm can be implemented through a simple and systematic design procedure. Finally, We have shown the result with a computer simulation by the present method which proposed the speed control system and stable operation and fairly transient performance. And then tt was found results by experimental process.