Abstract: A damping device for a stay cable including a rotating lever, a lever support saddle, a longitudinal connecting member, and a rigid connection rod. When the stay cable vibrates inside or outside the plane thereof, the vibration displacement is transferred to the rotating lever through the rigid connection rod. One end of the rotating lever is connected to the lever support saddle via the longitudinal connecting member, and can rotate up and down with the lever support saddle as the axis and rotate around its central axis. The other end of the rotating lever is connected to a mass block and a damper. The damping device effectively inhibits vibrations inside and outside the stay cable plane, is easy to install and maintain, and does not negatively impact the appearance of a cable-stayed bridge.