In this paper, an adaptive fuzzy-based global sliding mode control strategy is proposed for quadrotor unmanned aerial vehicles (UAVs) in robust trajectory tracking against parameter uncertainties and external disturbances. Compared with the conventional sliding mode control, the reaching phase and the control chattering are eliminated in the control scheme, and requirements of the upper bound of the uncertainties are removed. More specifically, in order to counteract the disturbances, the fuzzy system with multiple-input variables and continuous membership functions is adopted rather than the switching term, which softens the control signals greatly. Besides, the use of specific singletons membership functions for the multiple-output fuzzy sets simplifies the defuzzification and reduces the computation burden significantly. Additionally, an adaptive tuner is employed, and the optimal control efforts can be achieved. Finally, comparative flight performances under different controllers for the quadrotor UAVs are demonstrated to verify the effectiveness and superiority of the proposed control approach.