A nonsingular fast terminal sliding mode adaptive controller based on RBF neural network was proposed for trajectory tracking control of multi degree of freedom manipulator with slow convergence speed and low tracking precision. Firstly, the nonsingular fast terminal sliding mode hypersurface was adopted in the control scheme and the continuous terminal attractor was introduced into the switch control, which made the system converge to the equilibrium point in a finite time. Secondly, the adaptive RBF neural network was used to approximate the unknown nonlinear dynamics of the system, the adaptive compensation mechanism of approximation error and adaptive law of weights of neural networks were designed to realize the model free control. The global asymptotic stability and finite time convergence of the closed-loop system were proved by Lyapunov theory. Finally, the control method was applied to Denso serial manipulator for experimental verification, the effect of transmission delay on the experimental results was analyzed and the solution was proposed. The simulation and experimental results demonstrated that the proposed control method can improve the convergence speed and the tracking accuracy of the system effectively, and enhance the robustness of the external disturbance. At the same time, it can weaken the chattering of the system and enhance the real-time control.