According to the reversible principle of optical path, a computer generated half-circle view-able color rainbow holographic algorithm based on frequency domain synthesis is proposed. Firstly, the principle of half-circle view-able color rainbow hologram is analyzed, and the corresponding relationship between observation window and frequency domain is summarized. It is pointed out that the frequency spectrum of half-circle view-able color rainbow hologram object light is composed of the half-ring frequency spectrum of three primary colors. A plurality of projection images in a specific direction of a color three-dimensional object are used to separately perform color separation and interpolation, and perform a two-dimensional Fourier transform. The object light frequency spectrum of the half-circle view-able color rainbow hologram in the frequency domain is synthesized. And the synthesis object light frequency spectrum is transformed by two-dimensional inverse Fourier transform. Half-circle view-able color rainbow hologram is got by taking the real part and adding a bias component. Using this algorithm, a hologram with the area of 47 mm×47 mm and a resolution of 84000 pixel×84000 pixel is calculated and output by the holographic output system. Then it is followed by development, fixation and bleaching. Half-circle view-able color rainbow hologram with white light reconstruction is realized. The hologram shows vivid three-dimensional effect, brilliant colors, and can be watched by many people at the same time.