Holographic three-dimensional(3D) display can reconstruct the light field of a real scene, providing all depth cues and becoming one of the best solutions for true 3D display. Computer-generated holographic 3D display only needs to know the mathematical description of the object light wave, can flexibly control the wavefront, and display a virtual 3D object. However, the huge amount of data and the amount of calculations hinder the practical application of computer-generated holographic 3D display. This paper presented data compression coding techniques for multiple stages in computer-generated holographic 3D display, including sparse sampling of 3D objects, optimization and parameter optimization of holographic 3D video compression coding, holographic fractal compression algorithm, effectively reducing the amount of data. And the parallel computing capabilities of GPUs were utilized to enable fast calculation of holograms.