A backstepping non-singular fast-terminal sliding-mode-control method based on Finite-Time Disturbance Observer (FTDO) was proposed for a class of high-order nonlinear systems with unknown complex disturbances. The unknown complex disturbances was quickly and precisely estimated by FTDO and compensated by the designed robust items of the controller. The backstepping method was employed to deal with the high-order nonlinear system, and the dynamic surface control method was combined with it to design the virtual controller. A non-singular fast-terminal sliding-mode-controller was designed to improve the convergence speed and control accuracy of the system. The tracking error of the system has been proved to be uniform and ultimately bounded by using Lyapunov theorem. Finally, the simulation results demonstrated the effectiveness and feasibility of the proposed control method.