This paper proposes a new way of forming an aerial three-dimensional (3D) image that gives viewers smooth motion parallax. The proposed aerial 3D display is composed of an arc 3D display and aerial imaging by retro-reflection (AIRR), which features a wide viewing angle, a large-size scalability, and a low cost with mass-productive process. The arc 3D display consists of arc-shaped scratches on a transparent plastic plate. The principle of the arc 3D display is based on directional scattering. When a light impinges an arc-shaped scratch, the light is scattered mainly to the radial direction. The position of the bright spot on an arc scratch depends on the pupil position. The distance between the bright spots for both eyes on an arc scratches is proportional to the radius of curvature and is equivalent to the binocular parallax. Thus, by changing the radius of curvature, we can show a 3D image by use of a single LED illumination. This paper proposes an optical system to form an aerial 3D image with AIRR. AIRR consists of a light source, a beam splitter, and a retro-reflector. Arc scratches are illuminated by a quasi-parallel light that is generated by a Fresnel lens and a lightemitting diode (LED). In order to extract the directional scattered lights, we place the retro-reflector parallel to the beam splitter. The transmitted light does not impinge the beam splitter. Only the scattered lights reflect on the beam splitter and form the aerial image of the arc 3D display.