This paper presents a neural sliding mode control method for the mechanical arm with a non-singular inversion terminal in order to realize the trajectory tracking of a multi-joint robot arm with external interference and modeling errors. First, an inversion-sliding-mode controller with a non-singular terminal sliding surface is designed based on the inversion method and the principle of sliding mode control. Then, the radial basis function (RBF) neural network adaptive law is designed against the uncertainty in the inversion sliding mode control system due to its modeling errors and external interference. The upper bound of this uncertainty is estimated online. Finally, the stability of the control system is proved using the Lyapunov Theorem. Simulation analysis and experimental results show that the proposed method can not only eliminate the chattering phenomenon in the system, but also improve its tracking performance and robustness.