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This article aims to propose a novel neural adaptive control approach for the fixed-time attitude tracking of space vehicle subject to constrained outputs. The proposed controller is recursively synthesized by integrating with the barrier Lyapunov function (BLF) and neural approximation under the fixed-time backstepping control framework. The whole control design procedure involves two steps. In the first step, the virtual control signal is designed by adopting the BLF to guarantee the attitude tracking errors always within the predefined output constraints. In the second step, the actual control signal is designed by augmenting the neural network (NN) to approximate the uncertain term caused by unknown dynamics and disturbances. Theoretical analysis shows that the proposed controller can ensure all error signals in the closed-loop system stabilize to the small regions about the origin in fixed time even under unknown dynamics and disturbances. The effectiveness and excellent performance of the proposed control approach are validated by simulations and comparisons. [ABSTRACT FROM AUTHOR]