When the hook mass of tower crane can not be ignored, the dynamic system presents double-pendulum characteristics, which brings great challenges to the dynamic characteristics analysis and controller design of the crane systems. In this paper, an improved non-singular fast terminal sliding mode control with super-twisting algorithm (NFTSMC-STA) scheme is proposed to address the issues of double-pendulum effect,precise positioning,swing suppression and unexpected disturbances in crane systems. In order to reduce the chattering effect, a modified super-twisting algorithm (STA) is designed to ensure that the state variables reach the surface of the sliding mode in a finite-time. At the same time, a non-singular fast terminal sliding mode surface is established to ensure the finite-time convergence of the state variables on the sliding mode surface, and ultimately the finite- time convergence of the system state is guaranteed. In addition, adaptive compensation terms are employed to counteract the effects of unknown frictions. The stability of the closed-loop system is theoretically proved by using the Lyapunov technique. Simulation results and analysis show that the proposed method not only improves the chattering suppression effect significantly, but also has good positioning and swing suppression performance. And it has strong robustness to model uncertainties and external disturbances.