The problem of zero order diffraction (ZOD) in the computer generated hologram (CGH) is a commonly reported issue in employing computer generated hologram (CGH) systems. Failing to remove the zero order diffraction in either far-field or near-field region limits the display region or even worse, can destroy the reconstructed image. Therefore, the elimination of the ZOD is higly desired. The proposed new techniques to suppress the ZOD are the backbone of this thesis. We investigated ZOD sources in two different CGH systems and suggested different methods to remove the ZOD in each system. Two types of spatial light modulator (SLM) were employed for different type of CGHs, including a phase-only SLM and a binary amplitude-only SLM. All the proposed methods were examined with either simulation and experimental tests. For amplitude-only experiments, the ZOD suppression reached a factor of 3. Image quality and diffraction efficiency were also investigated for the proposed methods. / text