Disclosed are a fixing device and method of fixing substrate to provide holding means capable of surely fixing and positioning a sheet-like substrate even in vacuum, and to provide an operational mechanism thereof. A fixing device includes: a carrier plate for setting a glass substrate thereon; a claw for pressing the glass substrate set on the carrier plate, when the glass substrate is set thereon, by sandwiching the glass substrate from the periphery thereof; and an airbag having air sealed therein and expanding by lowering an external pressure. The claw is operated by using expansion of the airbag as power, thereby fixing the glass substrate.