In order to solve the attitude maneuver problem of rigid spacecraft, an adaptive second-order terminal sliding mode control algorithm was designed. A terminal sliding mode surface was designed to guarantee that the system states can converge to the original point along the sliding surface in finite time; a second-order terminal sliding mode controller was designed to overcome chattering, and an adaptive estimation parameter was adopted to compensate the external disturbances. The Lyapunov function methods proved that the designed algorithm can guarantee that the closedloop system is practically finite-time stable. The simulation results show that this algorithm can achieve fast response and high accuracy, can effectively restrain the system chattering and the external disturbance, and has important scientific significance and engineering value.