Demolition will clear the way for construction of a £60m, 10-storey office and ground floor retail scheme.
Contractor Dem-Master Demolition started soft stripping the cinema a few weeks ago and will tear down the cinema brick auditorium leaving the historic art deco facade and foyer, which will be incorporated into the Renfield Street scheme.
The 2800-seat venue, originally called the Paramount, became a landmark with its art deco lobby and white granite curved facade.
Joint developers Mountgrange and PRUPIM say the job will sustain around 150 construction jobs.