Steel lattice towers with suspended insulator strings are typically used to carry high-voltage overhead transmission lines. The installation of non-conductive power pylons made of glass fibre reinforced plastics enables a direct cable-pylon connection, as the composite structure acts as an unibody insulator. At the same time, wind-induced vibrations, such as the severe cable vibration phenomenon galloping, will consequently be directly transferred to the slender composite mast structure, potentially leading to extensive damage. The aim of the study is therefore to investigate the galloping behaviour of iced conductor lines with regard to different cable support conditions. Furthermore, additional damping in the composite power pylon structure is assumed to mitigate conductor line galloping and therefore reduce the risk of phase flash-overs between adjacent conductor lines. A numerical galloping simulation is carried out in order to evaluate the effect of a rigid cable-pylon connection with enhanced damping properties on the cable vibration amplitudes. A pylon-cable system, consisting of 3×300 m spans, is investigated. It was found that the support conditions of the conductor lines have a significant influence on the galloping mode, the vibration amplitudes and the orientation of the characteristic galloping ellipse. The addition of damping to the pylon decreases the vibration amplitudes slightly and leads to a re-orientation of the galloping ellipse.