A projector includes an illumination device, an electro-optic modulator, a projection optical system, a light source device having an ellipsoidal reflector, a light emitting tube, a collimator lens, a first lens array having plural first small lenses for dividing an illumination beam emitted from the light source device into plural partial beams, and a second lens array having plural second small lenses corresponding to the plural first small lenses of the first lens array. The light illumination device also includes a light cut-off member arranged in a position which is optically conjugate with the plural first small lenses and the elector-optic modulator between the illumination device and the electro-optic modulator, and has a predetermined opening part for adjusting the sectional shape of the illumination beam. The light illumination device further provides a rotating prism, which is arranged on the electro-optic modulator side of the light cut-off member, and scans the illumination beam from the light cut-off member, in synchronization with a frame rate of the electro-optic modulator.