In this paper, the problem of predefined-time attitude tracking control for a rigid spacecraft system in the presence of inertial parameter uncertainties and external disturbances is investigated. Based on the second-order dynamics model of the rigid spacecraft, a finite-time extended state observer is constructed by utilizing the fully actuated system theory. Then, a novel predefined-time attitude tracking control scheme is designed by introducing an adjustable parameter. The advantage of this control strategy is that the convergence time of the control system is not only smaller than the upper bound of the predefined time but also its speed can be directly adjusted by the introduced control parameter. By using the Lyapunov stability theory, this paper proves the convergence of the extended state observer and the stability of the closed-loop control system. Finally, the effectiveness of the designed control scheme is validated by numerical simulation.