This work addresses the challenging problem of finite-time fault tolerant attitude stabilization control for the rigid spacecraft attitude control system without the angular velocity measurements, in the presence of external disturbances and actuator failures. Consider the severe circumstances with above failures and uncertainties, a novel continuous finite-time Extended State Observer is first established to observe the attitude angular velocity and the synthetic failure simultaneously. Unlike the existing observers, the finite-time methodology and Extended State Observer are utilized, to achieve the finite-time uniformly ultimately bounded stability of the attitude angular velocity and extended state observation errors. Furthermore, a novel continuous finite-time attitude controller is developed by using the nonsingular terminal sliding mode control and super-twisting method. The main feature of this work stems from our use of multiply advanced techniques or methodologies that enables the finite-time stability of the closed-loop attitude control system and the designed control scheme is continuous with the property of chattering restraining. Finally, numerical simulation results are presented to illustrate the effectiveness and fine performances of the finite-time observer and controller for the attitude control system.