Based on the strain displacement relationship of spatial curved beam theory, a nonlinear dynamic equation for a hybrid model of iced bundle conductor galloping analysis with three translational degrees of freedom and one rotational degree of freedom was established. The element independence is numerically studied, and the impact of modal truncation on the galloping response is analyzed to verify the accuracy of the model. In addition, the compound damping cable is applied to transmission lines for the first time to prevent galloping, and a corresponding nonlinear vibration control finite element equation for the iced quad bundle conductor with a compound damping cable structure under wind load is developed. The study also examines the influence of various parameters on galloping amplitude. The results show that the hybrid model accurately predicts the galloping response of transmission lines. The compound damping cable can effectively suppress the galloping of the quad bundle conductor, and the vibration reduction effect reaches more than 85%. Increasing the installation height of the compound damping cable improves its damping effect. At the same installation height, when the horizontal installation position is close to the mid-span of the conductor, the damping effect first increases and then decreases, suggesting an optimal installation position exists. Moreover, properly increasing the stiffness of the primary cable and reducing the stiffness of the return spring can improve the vibration reduction effect of the compound damping cable. Additionally, if the damping coefficient and the mass of the primary cable are properly increased, the vibration reduction effect of the compound damping cable will be better.