This paper investigates the finite-time attitude tracking control problem for rigid spacecraft exposed to the external disturbance and unknown inertial parameters. Initially, the basic controller is developed under the assumption that the inertial parameters and the upper bound of external disturbances are available to the designer. However, this assumption is inapplicable in practical applications. Considering this limitation, adaptive laws and Minimum-learning- parameter (MLP) algorithm are employed in the second controller to estimate the unknown system dynamics. Finite-time stability for tracking errors is achievable under the proposed methods. Though theoretical analysis and numerical simulations, effectiveness of the proposed controllers has been validated.