An electron beam computed tomography system is provided that uses a cone beam geometry to generate truly three-dimensional images. The required cone beam projections can be obtained using a single sweep of the electron beam along the target ring (20). The target ring (20) is non-planar and shaped roughly like a 5/8th segment of the boundary curve of a saddle. The resulting source trajectory satisfies Tuy's completeness condition with respect to a sizeable volume of interest around the isocenter of the system. The detector (28) has a large area and is built from a plurality of small, brick-shaped detector modules (32), which are placed side by side along a detector trajectory that is a mirror image, through the isocenter, of the source trajectory. Owing to the special shapes of the target ring and the detector strip, a cone-beam of x-rays starting from the target ring and heading towards the opposite segment of the detector strip is not blocked by other portions of the detector.