A flexible glass display apparatus and a method for displaying image data in the apparatus are provided. The flexible glass display apparatus includes: a flexible glass display unit that displays image data portions; a sensing unit that detects bending of the display unit; another sensing unit that detects first and second areas which are brought into contact with each other due to bending of the display unit; and a controller, upon detection of contact between the first and second areas, controls at least one image data portion displayed in the first and second areas based on the contact, wherein an image data portion displayed in any one of the first and second areas is distinguishable in the other area.