This work investigates the anti-saturation attitude tracking control for the tailless aircraft with guaranteed output constraints, in presence of uncertain inertia parameters, bounded external disturbance, and actuator faults/failures. A predefined-time adaptive backstepping attitude control scheme has been proposed, the main features of this scheme lie in (a) designing a predefined-time filter to deal with the `explosion of complexity' and singularity problem; (b) introducing a nonlinear state-dependent function to handle the asymmetric time-varying output constraints; (c) compensating for the impact of the actuator faults/failures and input saturation by a nonlinear function and bounded estimation simultaneously. Moreover, the proposed control scheme can ensure all signals in the closed-loop system converge to a residual set around the origin within a predefined time, and this time constant can be set freely by the designer, independently of initial conditions. Finally, numerical simulations have been conducted to verify the performance of the proposed predefined-time fault-tolerant control scheme.