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 (brightness) of a light is reduced by an optical absorption and an S/N ratio is reduced by an increased white dispersion.A first lens array 18 and a second lens array 20 which are formed by disposing a plurality of half-cylindrical lenses 17, 19 in parallel on a common plain (a surface of a base member layer 13a) such that longitudinal directions of the cylindrical lenses 17, 19 should be orthogonal to each other. Unified lens array layer 13b and a shading layer 16 in which a section through which a light does not transmit is formed on a focal plain of the lens array layer 13b form a lens array sheet. Furthermore, fresnel lens are combined so as to form a transparent screen.