For practical holographic video display, it is important to generate holographic fringes as fast as possible. It is also important to display the full-color image with a simple display system. In our previous study, a full-color hologram was realized as a rainbow hologram, which discards the vertical parallax to reduce computation complexity. Its color reproduction, however, is not enough. Since this hologram uses the horizontal slit, proper color reproduction can be obtained only from a narrow viewing area in the vertical direction. In contrast, the image hologram provided a good contrast image, although it had only a single color. Also, the image hologram has full-parallax information. In this work, we investigate the image hologram for fast calculation and the display optics for full-color holograms with full parallax. Since image points are located close to the hologram, the required computation area of the image hologram becomes much smaller than that of the entire hologram. Therefore, vastly improved computational speed is obtained. The full-color hologram is displayed on a holographic video display system, which uses part of the original optics and liquid crystal on silicon (LCoS) panels of the conventional video projector to separate and combine color components. From the experimental results, we obtain a full-parallax reconstructed image and better color reproduction compared with the rainbow hologram.