A pneumatically operated active vibration damping device comprising a mounting member attachable to an object whose vibration is to be damped, a mass member elastically connected to the mounting member such that the mass member can be oscillated based on a periodic change of an air pressure in an air chamber connected to an air piping system, an active damping switch valve which is connected to the air piping system and which is operable for selective connection of the air chamber to a vacuum source and an atmosphere, to control a frequency and a phase of an oscillation of the mass member, and a pressure regulating switch valve connected to the air piping system, for alternately connecting and disconnecting the air chamber to and from the vacuum source and/or said atmosphere, so as to regulate a magnitude of said periodic change of said air pressure in said air chamber, for adjusting an amplitude of said oscillation of the mass member.