This paper investigates a finite-time adaptive attitude tracking fault-tolerant control problem for non-rigid spacecraft with actuator fault, time-varying inertia and external disturbances, and proposes an adaptive finite-time attitude tracking fault-tolerant control algorithm. Based on the finite-time theory and adaptive approach, a controller is designed to guarantee that the actuator fault attitude tracking system is finite-time stable. Furthermore, for overcoming the inertia uncertainties and rejecting the external disturbances, an adaptive system uncertainty estimation and disturbance estimation were designed to compensate the system respectively. The practical finite-time stability of the system is proved via Lyapunov stability theory. Numerical simulation results demonstrate the effectiveness of the proposed finite-time control strategy.