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In this paper, a first‐order approximation coupling (FOAC) model is investigated to analyze the dynamics of the hub‐beam system, which is based on the Hamilton theory and the finite element discretization method. The FOAC model for the hub‐beam system considers the second‐order coupling quantity of the axial displacement caused by the transverse displacement of the beam. The dynamic characteristics of the system are studied through numerical simulations under twos cases: the rotary inertia of the hub is much larger than, and is close to, that of the flexible beam. Simulation and comparison studies using both the traditional zeroth‐order approximation coupling (ZOAC) model and the FOAC model shows that when large motion of the system is unknown, possible failure exists by using the ZOAC model, whereas the FOAC model is valid. When the rotary inertia of the hub is much larger than that of the beam, the result using the ZOAC model is similar to that using the FOAC model. But when the rotary inertia of the hub is close to that of the beam, the ZOAC model may lead to a large error, while the FOAC model can still accurately describe the dynamic hub‐beam system.