In this paper, a non-singular fast terminal sliding mode control (NFTSMC) strategy based on a finite-time observer and improved reaching rate is proposed to solve the control problem of aerial robot systems subject to actuator faults and internal and external disturbances. Using the control strategy proposed in this paper, rapid convergence and high robustness of the system are guaranteed. In addition, the proposed finite-time observer can observe information related to the actuator fault or internal and external disturbance of the system in an accurate and timely fashion, and actively compensate the fault. The improved reaching law introduced in this paper can cause the system reach the sliding surface quickly, effectively improving the response speed of the system and increasing the tracking performance of the system. The stability of the whole system is proved using Lyapunov stability analysis. Finally, the effectiveness of the proposed control strategy is verified on the basis of a numerical simulation of a six-rotor UAV model with manipulator.