<p>Flexible-link manipulator is extensively used in mechanical engineering that requires human–machine interaction. However, currently, most control approaches for the flexible-link manipulator are designed based on accurate system model information, which has not only slow convergence rate but also low accuracy. Aiming at these problems, this paper proposes a novel adaptive model-free finite-time tracking control (FTTC) scheme with accelerated convergence speed for a class of multi-degree of freedoms (DoFs) flexible-link manipulators. Based on the singular perturbation theory, the closed-loop system is separated into a fast-subsystem (FSS) and a slow-subsystem (SSS). For the SSS, a new nonsingular integral fast terminal sliding mode (NIFTSM) is proposed to provide excellent error convergence as well as robustness. Moreover, the time delay estimation (TDE) method and adaptive finite-time disturbance observer (AFTDOB) are combined to achieve applicable high accuracy with different tracking commands and lumped system uncertainties. Besides, a finite-time super-twisting sliding mode control approach is designed to stabilize the FSS, which can be interpreted as the link vibrations. Eventually, finite-time zero-error tracking can be achieved without the requirement of the prior knowledge on the bound of the exact system dynamics and the parameter uncertainties. Simulation and experiment studies are conducted to verify the effectiveness of the proposed control algorithms. Numerous comparison results indicate that the proposed controller is chattering-free, high-precision, and robust.</p>