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This paper studies an observer-based adaptive learning control for spacecraft attitude stabilization subject to actuator fault, parameter uncertainty and external disturbance. Specifically, a new Barrier Function-based Iterative Learning Observer is proposed to estimate the lumped disturbance. Unlike existing iterative learning observer scheme, the newly proposed observer allows the gain matrix to fluctuate in accordance with exact values of the estimation errors, which leads to the estimation errors converges to a predefined neighborhood of zero independent of the adaptive gain matrix in finite time. Then, a composite control law is developed for spacecraft attitude stabilization by combining the newly proposed observer with a robust feedback controller. The stability of the overall closed-loop control system is proved in the Lyapunov framework. Finally, the robustness and effectiveness of the proposed strategy is demonstrated by numerical simulation. [ABSTRACT FROM AUTHOR]