This paper presents a practical nonsingular terminal sliding-mode (TSM) tracking control design for robot manipulators using time-delay estimation (TDE). The proposed control assures fast convergence due to the nonlinear TSM, and requires no prior knowledge about the robot dynamics due to the TDE. Despite its model-free nature, the proposed control provides high-accuracy control and robustness against parameters variations. The simplicity, robustness, and fast convergence of the proposed control are verified through both 2-DOF planar robot simulations and 3-DOF PUMA-type robot experiments.