Computed tomography based on high-resolution soft x-ray microscopy utilizes the natural contrast for biological specimens provided by the water window (lambda = 2.4 - 4.4 nm) and the high resolving power of zone plate objectives. It is capable of revealing the 3D structure of biological specimens at sub-visible-microscopic resolution. To date, the technique has only been available at synchrotron-based microscopes, which limits the researchers access. In the present paper we demonstrate high-resolution soft x-ray tomography with a laboratory zone-plate-based soft x-ray microscope. The specimen, a diatom mounted on a glass capillary, was reconstructed from a tilt series of 53 images covering 180 degrees using a filtered back projection algorithm. The resolution of the tomogram was estimated to a half period of 140 nm using a differential-phase-residual method. Cryo-fixation, increased source brightness and extended-depth-of-focus objectives are important for pushing the resolution of compact systems for biological samples.