This paper presents a discrete-time sliding mode control based on a properly designed state observer for a Permanent Magnet Synchronous Motor (PMSM). A cascade control scheme is proposed which provides accurate speed tracking performance. The asymptotical vanishing of the observation error and the ultimate boundedness of the speed tracking error are proved. The controller performances have been evaluated by simulation using the model of a commercial PMSM drive. Simulations show that the proposed observer based controller produces good tracking performances