A novel full parallax and viewing-angle enhanced computer-generated holographic (CGH) three-dimensional (3D) display system is proposed and implemented by combining an integral lens array and colorized synthetic phase holograms displayed on a phase-type spatial light modulator. For analyzing the viewing-angle limitations of our CGH 3D display system, we provide some theoretical background and introduce a simple ray-tracing method for 3D image reconstruction. From our method we can get continuously varying full parallax 3D images with the viewing angle about +/-6 degrees . To design the colorized phase holograms, we used a modified iterative Fourier transform algorithm and we could obtain a high diffraction efficiency (~92.5%) and a large signal-to-noise ratio (~11dB) from our simulation results. Finally we show some experimental results that verify our concept and demonstrate the full parallax viewing-angle enhanced color CGH display system.