A projector includes a projection section having a light source, a light modulation device and a projection lens, and modulating light emitted from the light source with the light device, and then projecting the light modulated through the projection lens to project a projection image on a screen, a projection optical system drive section for changing a projection position of the projection image, a projection control section for making the light device display a reduced input image, and a shift control section for controlling the projection optical system drive section wherein the projection position of the projection image when displaying the reduced input image at a central display position and at a shift display position become the same when the projection control section changes the display position of the reduced input image from the central display position to the shift display position in a display area of the light device.