A ray-driven backprojector is based on ray-tracing, which computes the length of the intersection between the ray paths and each voxel to be reconstructed. To reduce the computational burden caused by these exhaustive intersection tests, we propose a fully graphics processing unit (GPU)-based ray-driven backprojector in conjunction with a ray-culling scheme that enables straightforward parallelization without compromising the high computing performance of a GPU. The purpose of the ray-culling scheme is to reduce the number of ray-voxel intersection tests by excluding rays irrelevant to a specific voxel computation. This rejection step is based on an axis-aligned bounding box (AABB) enclosing a region of voxel projection, where eight vertices of each voxel are projected onto the detector plane. The range of the rectangular-shaped AABB is determined by min/max operations on the coordinates in the region. Using the indices of pixels inside the AABB, the rays passing through the voxel can be identified and the voxel is weighted as the length of intersection between the voxel and the ray. This procedure makes it possible to reflect voxel-level parallelization, allowing an independent calculation at each voxel, which is feasible for a GPU implementation. To eliminate redundant calculations during ray-culling, a shared-memory optimization is applied to exploit the GPU memory hierarchy. In experimental results using real measurement data with phantoms, the proposed GPU-based ray-culling scheme reconstructed a volume of resolution 28032803176 in 77 seconds from 680 projections of resolution 10243768 , which is 26 times and 7.5 times faster than standard CPU-based and GPU-based ray-driven backprojectors, respectively. Qualitative and quantitative analyses showed that the ray-driven backprojector provides high-quality reconstruction images when compared with those generated by the Feldkamp-Davis-Kress algorithm using a pixel-driven backprojector, with an average of 2.5 times higher contrast-to-noise ratio, 1.04 times higher universal quality index, and 1.39 times higher normalized mutual information.