The invention provides a half-wave plate, an optical pickup device, a polarization conversion element, and a projection display device, which are capable of improving transfer efficiency of a half-wave plate formed by a single crystal plate. The single crystal plate is made of an inorganic material having a birefringent property and rotatory power, wherein a polarization plane of linearly polarized light entering from an entrance surface of the crystal plate is rotated and then output from an exit surface of the crystal plate, the phase difference is disposed as gamma= 180degrees + correctingvalue gamma alpha, a cutting angle Beta of a quartz plate formed by a normal relative to the entrance surface and an optical axis is disposed as 5 degrees <= Beta <= 30 degrees, the correction value gamma alpha is determined according to a predetermined polynomial, the polynomial uses an optical axis azimuth angle Theta formed by an optical axis projection line formed by projection of the opticalaxis on the entrance surface and a polarization plane of linearly polarized light entering from the entrance surface, and the cutting angle Beta as variable quantities.