A robust adaptive fuzzy nonlinear controller based on dynamic surface and integral sliding mode control strategy (ADSISMC) is proposed to realize trajectory tracking for a class of quadrotor UAVs. In this study, the composite factors including parametric uncertainties and external disturbances are added to controller design, which make it more realistic. The quadrotor model is divided into two subsystems of attitude and position that make the control design become feasible. The main contributions of the proposed ADSISMC strategy are as follows: (1) The combination of dynamic surface and integral sliding mode makes the system always in sliding stage by finding the appropriate initial position compared with the common sliding mode, and the complexity of explosion in backstepping method is eliminated. (2) By introducing the fuzzy system, the unknown functions and uncertainties can be approximated which significantly improves the robustness and the tracking performance. (3) The switching control strategy is utilized to compensate for the errors between estimated and ideal inputs; the tracking performance of the whole system has been significantly improved. The simulation results show the effectiveness of the proposed control method.