Quadrotor unmanned aerial vehicles (UAVs) have broad application values in many areas. The flight control problems for this kind of system have been attracting the attention of researchers. This paper discusses the attitude tracking control problem for this mechanical system when the external unknown disturbances exist. We develop an adaptive super-twist sliding mode method. The method firstly constructs sliding mode functions for the system based on its flight control objectives. After that, the adaptive super-twist robust sliding mode controllers are designed. The control gains of the controllers can be dynamically adjusted. And the designed controllers drive the Quadrotor UAV to infinitely approach the sliding surface in finite time. It guarantees the motion control objectives of the Quadrotor UAV to be realized. Finally, simulation results verify the validity of the presented control strategy.