In this paper, a time-varying nonsingular terminal sliding mode (T-NTSM) controller is proposed and modified for the rigid robot manipulators with parametric uncertainties and external disturbances. First, in order to eliminate the reaching phase, a novel T-NTSM manifold is proposed by incorporating a piecewise defined function of time into a nonsingular terminal sliding mode manifold. Then a T-NTSM controller is derived from such a sliding surface, by which the robustness is ensured during the entire response of the system, and the convergence time can be chosen in advance. An especially effective method is provided for parameter selection to meet the convergence time requirement. Subsequently, a modified T-NTSM controller is proposed to enhance performance by introducing a time-varying gain in the proposed T-NTSM manifold. The modified controller ensures faster convergence rate and smaller control input amplitude. Finally, the proposed controllers are applied in the control of a two-link manipulator. All of the simulation results demonstrate the effectiveness of the proposed control methods.