With the space technology development, large flexible space deployable structures have been used widely. Studying on the vibration control for large flexible space deployable structures becomes very important. In this study, a novel passive vibration damping device is developed for the multi-panel sun-orientated deployable solar array. Its upper strut contains a viscous damper while the lower strut is rigid. The device is lockable and located near the solar array root hinge to increase the structural damping without reducing the fundamental frequency. This design will not influence the original functions of the solar array, such as folding, deploying, and sun tracking. The corresponding finite element models are established, and the properties of the damping device are investigated by modal analysis and transient response analysis. The damping mechanism design for a certain type of solar array is presented. The associated modal tests based on a solar array test sample verify the effectiveness of the device. Conclusions are drawn to help define design guidance for future damping device implementations.