A projector includes: a projection optical device; an exterior housing; a shutter; and a support member, the shutter and support member are provided with an engagement structure including an engagement protrusion which being provided on either one of them, protrudes along a vertical axis, and an engagement groove which being provided on the other, and extending in a direction in which the shutter moves, guides a movement of the engagement protrusion by the engagement protrusion being inserted therein, and the engagement groove is provided in such a way that a start end at which the engagement protrusion is positioned in the closed position is positioned to the projection optical device projection side of a finish end at which the engagement protrusion is positioned in the open position.