This paper deals with the problem of fixed-time attitude tracking control for spacecraft subject to model uncertainties and external disturbances. Firstly, by using a fixed-time extended state observer (Fx-TESO), the synthetic uncertainties generated by external disturbances and model deviations can be estimated and compensated accordingly. We propose a novel FxTESO aimed to improve previous methods. Compared with the existing extended state observer (ESO), the proposed FxTESO provides faster convergence and higher accuracy. Then, we design a fixed-time adaptive attitude tracking controller based on the strategy combining the FxTESO and fast non-singular terminal sliding mode control (FNTSMC), such that a desired attitude can be achieved accurately, which does not only allow providing fast and accurate responses, and acceptable chattering suppression, but also avoiding singularity. Finally, the numerical simulation results are discussed to verify the efficiency and merits of the proposed control strategy.