In this paper, results are presented for a study of finite-time attitude tracking control of a rigid spacecraft with actuator saturation constraints. By developing a methodology, which combines the idea of adding a power integrator with the adaptive technique, a novel continuous finite-time control scheme is proposed to ensure that the desired reference attitude is tracked within a finite time, even if under the actuator magnitude constraints. In addition, the proposed controller takes parametric uncertainties and external disturbances explicitly into consideration as well. In particular, with the help of adaptive technique, the exact inertia matrix is not necessary for the controller design and the external disturbances can be handled substantially. Besides detailed controller design processes and rigorous theoretical analysis of related finite-time stability, numerical simulation results are exhibited to demonstrate the effectiveness and benefits of the proposed control scheme.