The design of trajectory tracking controller for a quad-rotor Unmanned Aerial Vehicles (UAV) is difficult due to the UAV's inherent characteristics of under-actuation and strong coupling. Considering the model uncertainties and external disturbances, we designed a trajectory tracking controller for the quad-rotor UAVs with timing-varying mass and wind disturbance based on the idea of the control structure of the inner-outer loop. An adaptive sliding-mode controller was designed, which implemented the trajectory tracking in the outer loop and generated the expected lift force and attitude angle. The active disturbance-rejection control technique was adopted to design the inner-loop controller, which was used to follow the expected attitude angle. The simulation results of trajectory tracking in the presence of external disturbances prove the effectiveness and robustness of the designed controller.