Holographic display is capable of reconstructing the whole optical wave field of a three-dimensional (3D) scene. It is the only one among all the 3D display techniques that can produce all the depth cues. With the development of computing technology and spatial light modulators, computer generated holograms (CGHs) can now be used to produce dynamic 3D images of synthetic objects. Computation holography becomes highly complicated and demanding when it is employed to produce real 3D images. Here we present a novel algorithm for generating a full parallax 3D CGH with occlusion effect, which is an important property of 3D perception, but has often been neglected in fully computed hologram synthesis. The ray casting technique, which is widely used in computer graphics, is introduced to handle the occlusion issue of CGH computation. Horizontally and vertically distributed rays are projected from each hologram sample to the 3D objects to obtain the complex amplitude distribution. The occlusion issue is handled by performing ray casting calculations to all the hologram samples. The proposed algorithm has no restriction on or approximation to the 3D objects, and hence it can produce reconstructed images with correct shading effect and no visible artifacts. Programmable graphics processing unit (GPU) is used to perform parallel calculation. This is made possible because each hologram sample belongs to an independent operation. To demonstrate the performance of our proposed algorithm, an optical experiment is performed to reconstruct the 3D scene by using a phase-only spatial light modulator. We can easily perceive the accommodation cue by focusing our eyes on different depths of the scene and the motion parallax cue with occlusion effect by moving our eyes around. The experiment result confirms that the CGHs produced by our algorithm can successfully reconstruct 3D images with all the depth cues.