We propose a new optical system of glasses-free spherical 3D display and validity of the system is confirmed in this paper. The proposal display is light field display; a capable method to show 3D images to multiple viewers at once and perform complicated optical effect like occlusion effect. The proposal system is also capable to perform motion parallax effect in multiple directions (full-parallax). The proposal system is based on time-division multiplexing. The optical system consists of a rotating specially designed sphere-shaped flat mirror array and a high-speed projector. The rotating mirror array reflects rays from the projector to various angles. By controlling the intensity of the rays with the projector properly, a 3D image can be seen in the mirror array. From the results of the optical computer simulations using ray tracing method, expected 3D image was observed and we confirmed availability of the system as the 3D display. A prototype was developed using 3D printing and feasibility of the system was also confirmed. Additionally, color display of the same method was developed using 3 high-speed projectors.