This paper proposes a new control algorithm for a matrix converter based PMSM position control system. First, a new switching strategy, which uses neural-network learning technique, is proposed to reduce the current harmonics of the permanent magnet synchronous motor. Next, a non-linear adaptive backstepping control algorithm is proposed to improve the system performance. By using the proposed controller, the system performs well. It has a good transient response, load disturbance rejection capability, and tracking ability. A satisfactory servo drive, as a result, can be achieved. In addition, the realization of the controller is very simple. All the control loops, including current- loop, speed-loop, and position-loop, are implemented by a 32-bit TMS320C40 digital signal processor. The hardware, therefore, is very simple. Several experimental results are shown to validate the theoretical analysis.