Zirconium diboride (ZrB2) has a hexagonal crystal structure with an in-plane lattice constant of 3.168 Å, very close to that of GaN (3.189 Å). It is a metalloid compound and a very good electrical conductor, with a resistivity of 4.6 µΩcenterdotcm. We propose ZrB2 (0001) as an electrically conductive lattice-matched substrate for GaN. Firstly, bulk crystal growth of ZrB2 using a radio frequency (rf)-heated floating zone (FZ) method is presented. Relatively large crystals (phiv10 mm×60 mm) were obtained using this method. The thermal expansion coefficient and thermal conductivity of ZrB2 were evaluated using this crystal. Characterization of ZrB2 (0001) mirror-polished substrate was carried out by optical microscopic examination and X-ray diffraction. Finally, the results of heteroepitaxial growth are briefly mentioned.