The method is based on an adaptive flux observer in the rotor-speed reference frame, in which a second-order Kalman filter is employed to modify the estimated rotor flux to improve the performance of speed estimation. The Kalman filter modifies the estimated rotor flux based on the measured stator currents. The estimated speed is used in the speed feedback for vector control and in the co-ordinate transformation for current controller. The proposed method has the advantage of saving much computation time in comparison with the reduced-order extended Kalman filter. Compared with the conventional adaptive observer, the proposed method has the advantage of better accuracy to follow the speed command under heavy loads. Experimental results show the effectiveness of the proposed method.