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In this paper, we present an adaptive control strategy for the output-constrained attitude tracking of rigid spacecraft under unknown inertia and disturbances. The designed controller is recursively constructed under the framework of the backstepping method, which involves an auxiliary stabilizing law and a practical control law. In the auxiliary stabilizing law design, the log-type barrier Lyapunov function (BLF) is embedded to tackle the time-varying output constraints. In addition, in the practical control law design, the element-wise parametric adaptive laws are adopted to identify the unknown inertia and disturbances by introducing a linear mapping operator. The stability evaluation indicates that the overall closed-loop system is semi-globally uniformly ultimately bounded (SGUUB) and all error variables can eventually regulate to the minor fields about zero. Meanwhile, the spacecraft attitude tracking errors can be preserved in the preassigned output constraints. Lastly, the efficiency and strong robustness of the presented control strategy are demonstrated through competitive simulations. [ABSTRACT FROM AUTHOR]