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This paper focuses on the disturbance attenuation control of the quadrotor suspended payload system with unknown payload mass. Since the quadrotor transportation system is an eight-degree-of-freedom system with only four actuated degrees, it is difficult to achieve rapid stabilization of the quadrotor under varying payload and external disturbances. In this paper, a nonlinear controller based on rotation matrix is designed to rapid stabilization of attitude. By analyzing the effect of load mass on the trajectory tracking control, a parameter adaptive controller is proposed for position control. A mass estimation algorithm is established to estimate the payload mass in the air, which improves the robustness of the system. This approach can maximize load-bearing capacity within the thrust range of the quadrotor. The Lyapunov-based analysis proves the exponential convergence of the attitude error and the stability of the whole system. The contrast simulations demonstrate that the controller is superior to the sliding-mode controller incorporating input shaping on mass estimation, trajectory tracking, and disturbance resistance.