Abstract: Aiming at the singularity and slow-convergence problem of the existing terminal sliding mode(TSM) control, this paper proposes a nonsingular and fast terminal sliding function and proves its finite-time convergence property with Lyapunov method.On this basis,the control law is synthesized by employing an attractor with negative exponential factor to guarantee the time-continuous control input and global existence of the sliding mode.Theoretical analysis indicates that by selecting the control parameters properly,convergence stagnation of the closed system can be avoided and a preferable robustness can be obtained when the model error and the external disturbance are bounded.