In this article, an observer-based adaptive non-singular fast-reaching terminal sliding mode control strategy is proposed to tackle the problem of actuator faults and uncertain disturbance in aerial robot systems. Firstly, a model of an aerial robot system is established through dynamic analysis. Next, an adaptive observer, combined with a fast adaptive fault estimation (FAFE) algorithm, is proposed to estimate system states and actuator failure and compensate for faults in a precise and prompt manner. In addition, a non-singular fast terminal sliding surface is defined, taking into account the fast convergence of the tracking errors in order to provide appropriate trajectory tracking results. Since the upper bounds of the disturbances caused by the manipulator of the system in practice are unknown, the control approach may benefit from the addition of an adaptive control strategy that can suppress the influence of uncertain disturbances. The Lyapunov stability theory demonstrates that tracking errors are able to converge stably and quickly. In the end, the contrast experiment is conducted to exhibit the effectiveness of the proposed control strategy. The results demonstrate quicker convergence and improved estimating accuracy.