Oxide superconducting YBaCuO thin films were grown on Y-and Z-cut LiNbO3 (LN) electrooptic crystal substrates with and without buffer layers, and their film crystallinity was closely investigated by X-ray diffraction, transmission electron microscopy, reflection high-energy electron diffraction and Auger electron spectroscopy. Due to the intensive reaction, direct deposition of films resulted in poor quality. When sputtered (111)-MgO film was introduced as a buffer layer, significant diffusion of constituent atoms was unavoidable among YBaCuO, MgO and LN. As a result, the superconductivity of the YBaCuO layer was substantially degraded. The Y2O3-stabilized ZrO2 (YSZ) grown by sputtering, followed by wet O2 anneal, served as a good buffer layer for Y1Ba2Cu3Oy films on LN substrates, and epitaxial growth of (001)-Y1Ba2Cu3Oy with Tc0 = 89 K was reproducibly obtained on Y-cut LN substrates.