A Zernike-type phase-contrast X-ray microscope with a zone plate and a phase plate was constructed at the Photon Factory BL3C2. Parallel monochromatic X-rays of 8.97 keV were incident on a specimen and a direct beam transmitted through the specimen was focused on the back focal plane of the zone plate, where an aluminium phase plate was placed. Tantalum line patterns as fine as 0.3 microm could be imaged. Phase-contrast images of polypropylene wires and polystyrene latex beads were obtained, which showed better contrast than that of their bright field images.