In the adaptive neural control design, since the number of hidden neurons is finite for real-time applications, the approximation errors introduced by the neural network cannot be inevitable. To ensure the stability of the adaptive neural control system, a switching compensator is designed to dispel the approximation error. However, it will lead to substantial chattering in the control effort. In this paper, an adaptive dynamic sliding-mode neural control (ADSNC) system composed of a neural controller and a fuzzy compensator is proposed to tackle this problem. The neural controller, using a radial basis function neural network, is the main controller and the fuzzy compensator is designed to eliminate the approximation error introduced by the neural controller. Moreover, a proportional-integral-type adaptation learning algorithm is developed based on the Lyapunov function; thus not only the system stability can be guaranteed but also the convergence of the tracking error and controller parameters can speed up. Finally, the proposed ADSNC system is implemented based on a field programmable gate array chip for low-cost and high-performance industrial applications and is applied to control a brushless DC (BLDC) motor to show its effectiveness. The experimental results demonstrate the proposed ADSNC scheme can achieve favorable control performance without encountering chattering phenomena.