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This note investigates the finite-time attitude control problems for a single spacecraft and multiple spacecraft. First of all, a finite-time controller is designed to solve finite-time attitude tracking problem for a single spacecraft. Rigorous proof shows that the desired attitude can be tracked in finite time in the absence of disturbances. In the presence of disturbances, the tracking errors can reach a region around the origin in finite time. Then, based on the neighbor rule, a distributed finite-time attitude control law is proposed for a group of spacecraft with a leader-follower architecture. Under the finite-time control law, the attitude synchronization can be achieved in finite time.