Microtomography using the combination of microfocus x-ray source and the cone-beam technique is now becoming widely used in material science and in industry. Recently, the structural analysis of soft materials, such as polymer fibers and biological materials, is strongly required. A compact low-energy soft x-ray computed tomography (CT) instrument capable of soft material observation was developed, and the proof-of-concept system was constructed and evaluated. In this article, the authors describe an instrument that they developed for the x-ray CT of soft materials. A newly developed x-ray tube for generating the low-energy continuum soft x ray is also described. Tomographic observation examples of both biomaterials and industrial polymers are demonstrated.