This paper investigates a predefined-time tracking control strategy based on a learning observer for a kind of spacecraft subjects to external disturbance and actuator faults. First, a general systematic scheme of an improved adaptive learning observer is proposed. Based on the adaptive learning observer framework, a learning observer for spacecraft attitude system is designed to estimate the lumped disturbance in the system. Then, the disturbance estimation information is used to design the predefined-time tracking controller, so that the attitude angle of the system can track the command signal at the predefined time. The convergence time of the system can be preset by the parameters of the fault-tolerant controller and is independent of the initial state value of the system. Through the Lyapunov stability theory analysis, it is concluded that the designed fault-tolerant controller can ensure the predefined-time stability of the system. Finally, through numerical simulation and compared with the existing observer and finite time control schemes, the proposed scheme is proved to be effective and feasible.