A high-performance robust hybrid speed controller for a permanent-magnet synchronous motor (PMSM) drive with an on-line trained neural-network model-following controller (NNMFC) is proposed. The robust hybrid controller is a two-degrees-of-freedom (2DOF) integral plus proportional & rate feedback (I-PD) with neural-network model-following (NNMF) speed controller (2DOF I-PD NNMFC). The robust controller combines the merits of the 2DOF I-PD controller and the NNMF controller to regulate the speed of a PMSM drive. First, a systematic mathematical procedure is derived to calculate the parameters of the synchronous d-q axes PI current controllers and the 2DOF I-PD speed controller according to the required specifications for the PMSM drive system. Then, the resulting closed loop transfer function of the PMSM drive system including the current control loop is used as the reference model. In addition to the 200F I-PD controller, a neural-network model-following controller whose weights are trained on-line is designed to realize high dynamic performance in disturbance rejection and tracking characteristics. According to the model-following error between the outputs of the reference model and the PMSM drive system, the NNMFC generates an adaptive control signal which is added to the 2DOF I-PD speed controller output to attain robust model-following characteristics under different operating conditions regardless of parameter variations and load disturbances. A computer simulation is developed to demonstrate the effectiveness of the proposed 200F I-PD NNMF controller. The results confirm that the proposed 2DOF I-PO NNMF speed controller produces rapid, robust performance and accurate response to the reference model regardless of load disturbances or PMSM parameter variations.