The Three-Dimensional (3D) vision became widely known as familiar imaging technique now. The 3D display has been put into practical use in various fields, such as entertainment and medical fields. Development of 3D display technology will play an important role in a wide range of fields. There are various ways to the method of displaying 3D image. There is one of the methods that showing 3D image method to use the ray reproduction and we focused on it. This method needs many viewpoint images when achieve a full-parallax because this method display different viewpoint image depending on the viewpoint. We proposed to reduce wasteful rays by limiting projector’s ray emitted to around only viewer using a spinning mirror, and to increase effectiveness of display device to achieve a full-parallax 3D display. We propose a method by using a tracking viewer’s eye, a high-speed projector, a rotating mirror that tracking viewer (a spinning mirror), a concave mirror array having the different vertical slope arranged circumferentially (a concave mirror array), a cylindrical mirror. About proposed method in simulation, we confirmed the scanning range and the locus of the movement in the horizontal direction of the ray. In addition, we confirmed the switching of the viewpoints and convergence performance in the vertical direction of rays. Therefore, we confirmed that it is possible to realize a full-parallax.