An air passageway opening/closing device provided with a plurality of sheet members provided with openings and passageway blocking parts located at the two sides of these openings, wherein the lengths in a direction of door movement of the openings differ by predetermined amounts, when an adjacent smaller sheet member moves in the direction of door movement by a predetermined amount, the smaller sheet member and the adjacent larger sheet member move together, the opening ranges of two air passageways are determined by a position of movement of an opening of the smallest sheet member to which a driving force is added, and the blocking ranges of two air passageways are determined by superposition of the passageway blocking parts of the plurality of sheet members in a stepwise offset state.