This paper considers the motion control problem for a hovering quadrotor aircraft. First, the position dynamical equation and the attitude dynamical equation are introduced respectively. Then, a PD control law is first designed for the aircraft position system, which can guarantee that the quadrotor aircraft can reach a fixed point in 3D space. To obtain a faster convergent rate for the attitude control system, the finite-time control algorithm is then designed, which can guarantee that the desired attitude can be tracked by the real attitude in a finite time. Finally, the simulation results are given to demonstrate the efficiency of the proposed method.