This paper proposes an adaptive self-organizing Hermite-polynomial-based neural control (ASHNC) system which is composed of a neural controller and a supervisor compensator. The neural controller uses a self-organizing Hermite-polynomial-based neural network (SHNN) to approximate an ideal feedback controller. For the SHNN, the developed self-organizing approach is clearly and easily used for real-time systems and the parameter learning ability is effective with high convergence precision and fast convergence time. The supervisor compensator is designed to eliminate the approximation error between the neural controller and ideal feedback controller without chattering phenomena. Moreover, a proportional–integral (PI) type adaptation law is derived based on the Lyapunov stability theory; thus not only the system stability of the control system can be guaranteed but also the convergence of the tracking error can be speeded up. Finally, the proposed ASHNC system is applied to a chaotic system. Simulation results demonstrate that the proposed ASHNC system can achieve favorable control performance.