A lockable door structure, disposed on a case, wherein the case has an opening, and the case has a locking rib in a position adjacent to the opening, the lockable door structure comprising: a door cover, hinged to the case and corresponding to the opening, wherein the door cover has a first surface and a second surface opposite to each other, and the door cover has a displacement slot running through the first surface and the second surface; a first sliding member, slidably mounted on the first surface of the door cover, wherein the first sliding member slides relative to the door cover among a normal position, a release position, and a retaining position; a fastening member, slidably mounted on the second surface of the door cover, wherein the fastening member has a sliding slot, a catch portion, and at least one protrusion; and a second sliding member, slidably disposed on the fastening member, wherein the first sliding member runs through the displacement slot and the sliding slot to join the second sliding member, when the first sliding member is in the normal position, the catch portion catches the locking rib, and the second sliding member is located on a lateral side of the protrusion, when the first sliding member moves from the normal position to the release position, the first sliding member moves in the displacement slot, and presses a wall of the sliding slot to make the catch portion depart from the locking rib, and when the first sliding member moves from the normal position to the retaining position, the first sliding member moves in the displacement slot to drive the second sliding member to move from the lateral side of the protrusion to be on the protrusion, so that the second sliding member is pressed by the protrusion to drive the first sliding member to press towards the first surface of the door cover. a door cover, hinged to the case and corresponding to the opening, wherein the door cover has a first surface and a second surface opposite to each other, and the door cover has a displacement slot running through the first surface and the second surface; a first sliding member, slidably mounted on the first surface of the door cover, wherein the first sliding member slides relative to the door cover among a normal position, a release position, and a retaining position; a fastening member, slidably mounted on the second surface of the door cover, wherein the fastening member has a sliding slot, a catch portion, and at least one protrusion; and a second sliding member, slidably disposed on the fastening member, wherein the first sliding member runs through the displacement slot and the sliding slot to join the second sliding member, when the first sliding member is in the normal position, the catch portion catches the locking rib, and the second sliding member is located on a lateral side of the protrusion, when the first sliding member moves from the normal position to the release position, the first sliding member moves in the displacement slot, and presses a wall of the sliding slot to make the catch portion depart from the locking rib, and when the first sliding member moves from the normal position to the retaining position, the first sliding member moves in the displacement slot to drive the second sliding member to move from the lateral side of the protrusion to be on the protrusion, so that the second sliding member is pressed by the protrusion to drive the first sliding member to press towards the first surface of the door cover.