We demonstrate a tomographic imaging modality that uses pulsed terahertz (THz) radiation to probe the optical properties of three-dimensional (3D) structures in the far-infrared. This THz-wave computed tomography (T-ray CT) system provides sectional images of objects in a manner analogous to conventional CT techniques such as x-ray CT. The transmitted amplitude and phase of broadband pulses of THz radiation are measured at multiple projection angles. The filtered backprojection algorithm is then used to reconstruct the target object, including both its 3D structure and its frequency-dependent far-infrared optical properties.