For the finite-time robust control of a rigid robot manipulator, a new adaptive non-singular fast terminal sliding mode control method is proposed.This method combines non-singular fast terminal sliding mode control with adaptive law.Firstly, the non-singular fast terminal sliding surface is selected, which is used to accelerate the convergence rate of trajectory tracking error of manipulator and solve singular problems in terminal sliding surface.Then, hyperbolic tangent function replaces sign function to reduce chattering of control input.Moreover, the adaptive law estimates the unknown external disturbance and uncertainties, so as to achieve trajectory tracking with unknown lumped disturbance.It is proved that the robot manipulator system can converge stably in finite time by establishing the Lyapunov function.Finally, the simulation results of a two-DOF robot manipulator are presented to illustrate the effectiveness and robustness of the proposed control method.