Rain-wind induced cable vibration can cause serious problems in cable-stayed bridges. Externally attached dampers have been used to provide an effective means to suppress the vibration of relatively short stay-cables. For very long stay-cables, however, such damper systems are rendered ineffective, as the dampers need be attached near the end of cables for aesthetic reasons. This paper investigates a new stay-cable damping system to mitigate the cable vibration. The proposed damping system which consists of a laminated rubber bearing and an internal damper may be installed inside of the cable anchorage. A simple analytical model of the cable-damper system is developed first based on the taut string representation of the cable. The response of a cable with the proposed damping system is obtained and then compared to those of the cable with and without an external passive damper. The proposed stay-cable damping system is shown to perform better than the optimal passive viscous damper.