A damping device for a main rope suspending a car of an elevator includes a coupled, a first pulley and a drive. The coupler is attached to the main rope above the car, and is configured to be pulled, in response to vibrations of the main rope, with a damping rope so as to suppress vibrations of the main rope. The first pulley is supported at a same height as a height of the coupler. The drive is configured to suppress vibration of the main rope by pulling a first damping rope coupled to the coupler and passing over the first pulley.