A new nonsingular fixed-time sliding mode control method is proposed for the trajectory tracking control of the manipulator under the influence of such factors as unmodeled dynamics and random interferences.Firstly, the dynamic equation of the n degree-of-freedom manipulator is derived by using Kanes equation and virtual work principle.Secondly, a new fixed-time sliding mode surface is designed based on the fixed-time stability theory.Combined with 6R manipulators Kane dynamics model, a non-singular fixed-time sliding mode controller is designed aiming at the uncertainty of model parameters and external interferences of the manipulator.The stability of the system is proved by using Lyapunov method.Numerical simulation shows that the designed controller can ensure that the convergence of the system state is independent of the initial conditions, and it has faster convergence rate, shorter convergence time and good robustness.