The relative oscillation between the strands of the suspension bridge hangers could be effectively mitigated by means of rigid spacers, but the hanger-spacer system may experience overall translational or torsional vibrations. In this paper, based on a four-strand hanger of the Xihoumen Bridge, the ANSYS software was utilized to establish three kinds of computational models for the hanger-spacer-damper system, and a series of free vibration analyses were carried out to study the characteristics of the universal curve for the torsional modes considering the effects of support stiffness and damper stiffness. The results show that the universal curves are affected by the torsional modes, and a unified universal curve cannot be used for the design of the dampers for different torsional modes. The realizable maximum damping ratio for torsional mode and its corresponding damper coefficient reduce with the decrease of the support stiffness. However, the realizable maximum ratio for torsional mode decreases with the increase of the damper stiffness, but its corresponding damper coefficient increases.