Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/302982 Open Access ; The problem of finite-time control for attitude tracking maneuver of a rigid spacecraft is investigated. External disturbance, unknown inertia parameters are addressed. As stepping stone, a sliding mode controller is designed. It requires the upper bound of the lumped uncertainty including disturbance and inertia matrix. However, this upper bound may not be easily obtained. Therefore, an adaptive sliding mode control law is then proposed to release that drawback. Adaptive technique is applied to estimate that bound. It is proved that the closed-loop attitude tracking system is finite-time stable. The tracking errors of the attitude and the angular velocity are asymptotically stabilized. Moreover, the upper bound on the lumped uncertainty can be exactly estimated in finite time. The attitude tracking performance with application of the control scheme is evaluated through a numerical example.