A fixed-time sliding mode control method based on the radial basis function(RBF) neural network is proposed for trajectory tracking control of multi-joint robots with typical nonlinear characteristics. Firstly, the dynamic model of multi-joint robots including system model uncertainty and external disturbance is established based on the Kane method. A sliding mode controller with fixed-time convergence is designed according to the dynamic model of the robot, the RBF neural network is used to approximate the uncertainties in the system model. The Lyapunov theory is used to prove that the tracking error of the system can converge in a fixed-time. Finally, a virtual prototype of a certain type of multi-joint robot is simulated and analyzed. Compared with the finite-time sliding mode controller based on the RBF neural network, the proposed controller has good tracking performance and can ensure that the system state converges in a fixed-time.