Provided are an apparatus and method of operating a multi-changer of an optical disc player which restricts an initial operation of the multi-changer of the optical disc by referring to a disc chucking and tray open/close states. According to the method, it is determined whether a type of a disc, which is currently mounted in the disc mounting unit, has been determined before, if a tray open or close key is inputted. If it is determined that the type of the disc has not been determined before, the tray is opened or closed. Then, if the tray is closed, the type of the disc is determined after chucking the disc which is currently mounted in the disc mounting unit. According to the method, it is possible to stabilize a player by restricting an initiating operation of the multi-changer of the optical disc, which occurs needlessly due to a tray open/close key, when a disc is not yet chucked.