**Featured Application: The proposed technique has potential for head mounted near-eye VR or AR applications.**

**Abstract:** A fast computer-generated holographic method with multiple projection images for a near-eye VR (Virtual Reality) and AR (Augmented Reality) 3D display is proposed. A 3D object located near the holographic plane is projected onto a projection plane to obtain a plurality of projected images with different angles. The hologram is calculated by superposition of projected images convolution with corresponding point spread functions (PSF). Holographic 3D display systems with LED as illumination, 4f optical filtering system and lens as eyepiece for near-eye VR display and holographic optical element (HOE) as combiner for near-eye AR display are designed and developed. The results show that the proposed calculation method is about 38 times faster than the conventional point cloud method and the display system is compact and flexible enough to produce speckle noise-free high-quality VR and AR 3D images with efficient focus and defocus capabilities.

**Keywords:** holographic 3D display; computer generated holography; augmented reality; virtual reality
