We have investigated the floating full color image display with the computer-generated hologram (CGH). The floating image, when utilized as a 3D display, gives strong impression to the viewer. In our previous study, to change the CGH shape from the flat type to the half cylindrical type, the floating image from the output CGH has the nearly 180 degrees viewing angle. However, since the previous CGH does not have wavelength-selectivity, reconstructed image only has a single color. Also, the huge calculation amount of the fringe pattern is big problem. Therefore, we now propose the rainbow-type computer generated alcove hologram. To decrease the calculation amount, the rainbow hologram sacrifices the vertical parallax. Also, this hologram can reconstruct an image with white light. Compared with the previous study of the Fresnel type, the calculation speed becomes 165 times faster. After calculation, we print this hologram with a fringe printer, and evaluate reconstructed floating full color images. In this study, we introduce the computer-generated rainbow hologram into the floating image display. The rainbow hologram can reconstruct full color image with white light illumination. It can be recorded by using a horizontal slit to limit the vertical parallax. Therefore, the slit changes into the half cylindrical slit, the wide viewing angle floating image display can reconstruct full color image.