Disclosed herein is an organic light-emitting display (OLED) device that includes: a substrate having an active area and an inactive area surrounding the active area; a first planarization layer flattening a surface on circuit elements in the active area and inactive area; an organic light-emitting element on the first planarization layer; an encapsulation element on the organic light-emitting element and the first planarization layer, the encapsulation element having a first inorganic layer, a second inorganic layer and an organic layer between the first and second inorganic layers; and a structure in the inactive area and spaced apart from the first planarization layer. The structure includes a first layer made of a same material as the first planarization layer; a plurality of walls on the first layer and spaced apart from each other; and a second layer that fills a space between the plurality of walls.