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In computational integral imaging (II), the elemental images are processed on serial processors to reconstruct one plane (slice) of the 3D scene. In this paper, we present a fast three-dimensional (3D) integral imaging system via a graphics processing unit (GPU) which allows parallel processing with multiple processors. We show that it can significantly accelerate 3D scene reconstruction in II using the GPU based stream-processing model. The streaming version of the ray back propagation algorithm with lookup table is presented. It is demonstrated that the ray back propagation algorithm with a lookup table for the 3D scene reconstruction in II to be processed on parallel processors may greatly improve computational speed while requiring minimally larger memory space as compared with CPU sequential computing. Experimental results verify the feasibility for parallel implementation of 3D integral imaging. To the best of our knowledge, this is the first study on achieving a 3D computational integral imaging system using GPU computing with high parallelism.