A leg structure of a desk constructed to provide a stronger durability at places such as kindergarten, children's house and the like and to conform to body shape of a user such as child, thereby facilitating to easily adjust height of an upper plate, which comprises a plurality of leg members; a male screw part screwed to one end of the leg members with a bolt part externally protruded at the center thereof; a female screw part screwed to the other end of the leg members with a nut part at the center thereof to be coupled with the bolt part of the male screw part, so that a plurality of leg members with the male and female screw parts coupled at both sides thereof are sequentially connected to form a leg of a desk; a coupling unit having a bottom side coupled with an upper end of the leg, a flange part formed at an upper side to be coupled to an upper plate with a plurality of screws and a fitting protruder formed at the top center of the flange part; and a fitting groove formed at the bottom surface of an upper plate for insertion of the fitting proturder.