Based on the strain-displacement relationship of the spatial curved beam theory， a galloping model for an iced single conductor with four degrees of freedom was established. The dynamic equation of the iced single conductor was constructed using the principle of virtual work. Element independence was verified through numerical calculations， and the impact of modal truncation on the galloping response was analyzed， verifying the accuracy of the model. In addition， the compound damping cable was used for the anti-galloping device of transmission lines， and a nonlinear vibration control finite element equation for an iced single conductor structure was established with a compound damping cable. The influence of relevant parameters on the galloping amplitude of the conductor was analyzed. The research results indicate that the galloping model of the iced single conductor can predict the galloping response of transmission lines. The compound damping cable can effectively suppress the galloping of a single conductor and achieve a damping rate of over 85%. The higher the installation height of the compound damping cable， the better the vibration reduction effect of the compound damping cable. However， at the same installation height， when the horizontal installation position is close to the mid-span of the conductor， the vibration reduction effect first increases and then decreases， indicating that there is an optimal installation position. Simultaneously 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. In addition， appropriately increasing the damping coefficient and the mass of the primary cable leads to better vibration reduction effect of the compound damping cable.