A flap door includes a door body configured to be rotated around a longitudinal axis of a shaft by extension of a gas lift. A guide cam is fixed to a sidewall and has the shaft rotatably mounted to a center of the guide cam in a direction perpendicular to the sidewall, and a guide groove is formed in a side of the guide cam. A first arm has one end fixed to the shaft and another end extended toward the gas lift. A second arm has one end connected to the shaft so as to be rotatable around the shaft and another end connected to an end of the gas lift. A rotation transferring member transfers a rotational force from the second arm to the first arm as the rotation transferring member moves along a slot formed in the second arm and simultaneously moves along the guide groove according to rotation of the second arm.