A projector includes: an optical modulation device configured to modulate an incident luminous flux; a projection optical device configured to project the luminous flux modulated by the optical modulation device; and a cooling device configured to cool the optical modulation device, wherein the cooling device includes a cooling fan, and a duct having a discharge portion that causes the air discharged from the cooling fan to circulate in a direction approximately parallel to the optical axis, and discharges it to a lateral side of the optical modulation device, and the duct is disposed in a state that, when the projection optical device and discharge portion are cut by a plane perpendicular to the optical axis, the height position of a first center between the upper end and lower end of the cross-section of the discharge portion and that of the optical axis differ from one another.