A lens array sheet, a transparent screen using the same, and a rear-projection display device are provided in which it is possible to control a perspective angle for the image in both a horizontal direction and a vertical direction without causing a problem in that a gain of a light is reduced by an optical absorption and an S/N ratio is reduced by an increased white dispersion. First lens and second lens arrays are formed by disposing a plurality of half-cylindrical lenses in parallel on a common plane such that longitudinal directions of the cylindrical lenses should be orthogonal to each other. A unified lens array layer and a shading layer in which a section through which a light does not transmit is formed on a focal plane of the lens array layer form a lens array sheet. Furthermore, fresnel lenses are combined so as to form a transparent screen.