Because an electric scooter driven by permanent magnet synchronous motor (PMSM) servo system has the unknown nonlinearity and the time-varying characteristics, its accurate dynamic model is difficult to establish for the design of the linear controller in whole system. In order to conquer this difficulty and raise robustness, a novel adaptive recurrent Legendre neural network (NN) control system, which has fast convergence and provide high accuracy, is proposed to control for PMSM servo-drive electric scooter under external torque disturbance in this study. The novel adaptive recurrent Legendre NN control system consists of a recurrent Legendre NN control with adaptation law and a remunerated control with estimation law. In addition, the online parameter tuning methodology of the recurrent Legendre NN control and the estimation law of the remunerated control can be derived by using the Lyapunov stability theorem. Finally, comparative studies are demonstrated by experimental results in order to show the effectiveness of the proposed control scheme.