The invention provides a mass damping device of a rigid connection space lever. By using the mass damping device, the vibration displacements inside and outside a cable surface of a stay cable are transferred to a rotating lever by a rigid connection rod; one end of the rotating lever is connected with a lever supporting seat through a longitudinal connecting element and can rotate up and down around the lever supporting seat and rotate around a self central shaft, while the other end is connected with a mass block and a damper; when the inside and the outside of cable surface of the stay cable vibrate, the vibration displacements are transferred to the rotating lever through the rigid connection rod to drive the rotating lever, the mass block and the damper to rotate up and down or rotate around the central shaft of the rotating lever and generate inertial force, elastic force and damping force; and when the outside of the stay cable rotates, the high-damping combination of the leversupporting seat and the longitudinal connecting element also provides rotational frictional resistance and viscous force, and through the amplification by the rotating lever, the rotational frictional resistance and the viscous force are transferred back to the stay cable through the rigid connection rod so as to change the mode quality, the rigidity and the damping of the stay cable and effectively inhibit the vibrations inside or outside the cable surface of the stay cable. The mass damping device is convenient to mount and maintain and has small influence on a landscape.