An operation-mode conversion apparatus for an image display compound device includes a power-state detector which detects a power state of the compound device, an operation-mode determination unit which determines a present operation mode of the compound device, and an operation-mode controller which converts the operation mode of the compound device based on the power state, the present operation mode, and whether one of an optical storage medium and a movable memory is detected by the compound device, in response to a user input signal, regardless of the preset operation mode.