This paper studies practical tracking control design of robot manipulators with continuous fractional-order nonsingular terminal sliding mode (CFONTSM) based on time-delay estimation (TDE). The proposed control design requires no detailed information about the robot dynamics, leading to an attractive model-free nature thanks to TDE, and ensures fast convergence and high tracking precision under heavy lumped uncertainties due to the FONTSM surface and fast-TSM-type reaching law. Stability of the closed-loop system and finite-time convergence are analyzed using Lyapunov stability theory. Comparative 2-DOF (degree of freedom) simulation and experiment results show that the proposed control design can ensure higher tracking precision and faster convergence compared with TDE-based continuous integer-order NTSM (CIONTSM) design in a wide range of speed; meanwhile, better performance is also observed compared with TDE-based IONTSM and FONTSM control designs using a boundary layer technique.