In this paper, trajectory tracking for a quadrotor unmanned aerial vehicle (UAV) is considered in the presence of a cable-suspended payload and wind as unknown disturbances. It is assumed that the wind disturbance is slowly time varying and affects quadrotor position and orientation independently. Nonlinear robust strategies, such as backstepping and sliding mode control could be used for trajectory tracking; however, they fail to stabilize the system in the presence of payload or wind, or both together. We have proposed a combined backstepping and super-twisting integral sliding mode strategy to stabilize the system. Conventional sliding mode control suggests discontinuous control signals and suffers from the chattering phenomenon whereas its super-twisting integral version suggests continuous control signals, which makes it implementable and chattering free.