This paper describes a proposal for a compact x-ray source based on parametric x-ray radiation (PXR). The PXR, which is produced when a single crystal is bombarded with relativistic electrons, has good monochromaticity and spatial coherence, and is expected to be well suited for imaging of low-Z materials and medical application. The proposed system employs a pair of copper accelerating structures which are operated at a cryogenic temperature of 20 K and arranged to form a resonant ring configuration. The electron beam is once accelerated up to 75 MeV in one of the structures, being decelerated down to lower than 7 MeV in the other structure after generating PXR at a single crystal, and then dumped. The expected x-ray yield is 10 9 photons=s at a center energy of 15 keV or higher.