This paper proposes a fault-tolerant nonsingular fixed-time control scheme based on neural networks (NNs) for spacecraft maneuver mission subject to actuator faults, unknown external disturbance and parametric uncertainty. The pose dynamic model of the rigid spacecraft is derived with unknown external disturbance and parametric uncertainty. A novel adaptive neural control law is proposed to estimate and compensate for the lumped system faults or uncertainties. Based on the adaptive neural control law, a nonsingular fixed-time terminal sliding-mode (NFTSM) controller is developed to ensure the fixed-time stability of the closed-loop system via the Lyapunov analysis. The singularity in the controller design can be directly avoided with no prior knowledge of lumped disturbance’ upper bound. The controller can speed up the convergence rate with improved control accuracy. Moreover, the settling time for the system states is independent of the initial conditions. Finally, comparative simulations are carried out to prove that the proposed control scheme has strong robustness and fault tolerance.