Disclosed are a portable electronic device having a display unit which can be bent or folded partially or wholly, and a control method thereof. The portable electronic device includes: a display unit having a front surface and a rear surface, and formed to be flexible; and a folding unit including a plurality of blocks and a connection unit, and configured to be foldable together with the display unit, the plurality of blocks overlapped with each other on the rear surface of the display unit, the connection unit configured to connect the plurality of blocks to each other, wherein the plurality of blocks are arranged such that at least part thereof is relatively-movable with respect to neighboring blocks in a direction to become far from or close to the neighboring blocks.