A method to reconstruct computer generated true color rainbow hologram is presented. Based on the principle of diffraction and geometric optics, the relationship between the observing window in spatial domain and its corresponding window in spatial frequency domain is analyzed. The illumination beams (red, green and blue light) are constructed and multiplied by rainbow hologram respectively. The multiplied results are analyzed in spatial frequency domain with Fourier transform. The spectral information corresponding to a specific perspective window is extracted by filtering in spatial frequency domain. And then the inverse Fourier transform is introduced to obtain the reconstructed image in the hologram plane. The reconstructed images in different positions are obtained from the object wave diffracting a given distance. The experimental results prove the validity of the proposed method. It opens up a new way to evaluate the correctness of computer generated true color rainbow hologram fast and economically.