For the control problem of nonlinear systems with multiple unknown nonlinear terms, a neural network based on Chebyshev orthogonal functions is proposed to realize the robust control of the system. In the study, a controller based on the neural network filter using Chebyshev orthogonal functions is proposed. Under bounded conditions of weight learning errors and tracking errors, the proposed control method can determine the weights of the controller and ensure the H_∞ robust control of nonlinear systems by using the Lyapunov stability theorem. Finally, for a nonlinear system, the proposed algorithm is used to determine the filter and the controller. The simulation results show the effectiveness of the proposed method.