This paper proposes a novel nonlinear H∞ control strategy for the suspended transport system of dual quadrotor UAVs, aimed at achieving precise trajectory tracking under unknown disturbance. First, based on the Euler-Lagrange method, a non-redundant model of the dual quadrotor UAVs’ suspended transport system is established. Then, a hierarchical control structure is designed. For the outer loop subsystem, a new nonlinear H∞ control strategy is proposed, where the integration effect of the all DOF is considered in the state space, and a nonlinear H∞ controller is designed in the weighted Sobolev space. The stability of the closed-loop system is then proved through the Lyapunov theorem. For the inner loop subsystem, Active Disturbance Rejection Control (ADRC) is employed. Finally, comparative simulation results highlight that the proposed controller outperforms existing methods in terms of control performance and robustness.