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List-mode processing is an efficient way of dealing with the sparse nature of PET data sets, and is the processing method of choice for time-of-flight (ToF) PET. We present a novel method of computing line projection operations required for list-mode ordered subsets expectation maximization (OSEM) for fully 3-D PET image reconstruction on a graphics processing unit (GPU) using the compute unified device architecture (CUDA) framework. Our method overcomes challenges such as compute thread divergence, and exploits GPU capabilities such as shared memory and atomic operations. When applied to line projection operations for list-mode time-of-flight PET, this new GPU-CUDA implementation is 188X faster than a single-threaded reference CPU implementation. Image quality is preserved with root mean squared (RMS) deviation of 0.05% between CPU and GPU-generated images, which has negligible effect in typical clinical applications.