ZnO thin films have been epitaxially grown on LiNbO3 (0001) substrates by rf magnetron sputtering. The crystallinity was examined by Xray diffraction. The omega-rocking curve full width at half-maximum for the ZnO (0002) reflection for films grown at 550 degrees C was 0.46 degrees. The epitaxial relationship between the ZnO film and the LiNbO3 substrate was determined to be [11 (2) over bar 0] ZnO//[10 (1) over bar 0] LiNbO3. The lattice mismatch for this orientation is about 9%, while it is about 18% for ZnO films on sapphire (0001) substrates. The temperature necessary for epitaxy was found to be lower than that required for films grown on sapphire.