This paper addresses the problem of robust fault-tolerant control of spacecraft attitude stabilization in the presence of model uncertainties, actuator failures, and external disturbances simultaneously. Utilizing the fast nonsingular terminal sliding mode control technique, a novel finite-time extended state observer is first proposed to estimate and compensate for the specified synthetic uncertainties derived from actuator failures and/or model deviations. And also the detailed derivations of the observer are provided, along with a thorough analysis for the associated ultimately bounded stability and estimation error convergence property in the sense of finite-time control. Then, with the reconstructed information achieving from the finite-time observer, an adaptive robust sliding mode based fault-tolerant control approach is developed to ensure that the closed-loop attitude control system reach the real sliding mode surface in finite time. Meanwhile, the chattering problem has been restrained via the modified gain adjusting law. The key feature of the proposed strategies is that the whole closed-loop fault-tolerant control system can be guaranteed theoretically to be finite-time stable by the development of Lyapunov methodology. Finally, numerical simulation results are presented to illustrate and highlight the fine performance benefits obtained using the proposed schemes.