Generation and reconstruction of computer-generated hologram(CGH) of images display on spherical surface by use of conformal maps is presented. Usually the reconstructed image is located on a planar plane when the hologram is illuminated by a plane wave. Conformal maps are corresponding relationship between planar and curved surface and widely used in computer graphic. Comparing with simply coordinates transversing, Conformal Maps have many advantages, such as they make the invariability of geometric form between origin images and reconstructed one. We combined conformal maps with the generation of CGH, realized the generation of computer-generated hologram of a two dimensional (2-D) image which displays on spherical surface and reconstructed the original image from generated CGH, therefore, realized the computer simulation of holographic record and reconstruct process. As reconstruction of a 2-D image on a spherical surface actually creates a three dimensional (3-D) displays, this technique may plays an important role in attempts at reconstruction of 3-D images from CGHs.