Adaptive back stepping control technique may provide robust control characteristics under parameter perturbation caused by changing external condition. In order to synthesize a high-precision velocity controller for IPMSM(Interior Permanent Magnet Synchronous Motor) using this method, the period of control loop should be very small. However, because of the resolution of the encoder for speed measurement, control cycle is limited, which makes it difficult to improve the performance of the controller. This paper proposes a velocity controller design method based on nonlinear adaptive back-stepping method to accomplish fast and accurate performance. Here, an EKF(Extended Kalman Filter) method is incorporated for the estimation of the motor speed into the design of a speed controller using adapted back-stepping control technique. The performance of the proposed controller is demonstrated through simulation using PSIM.