This study focused on structural and optical properties of ZnO films grown epitaxially on Gd3Ga5O12 substrates. ZnO films (a = 3.2439 Å and c = 5.2036 Å) were deposited on the (001) and (111) planes of Gd3Ga5O12 (GGG: a = 12.383 Å) garnet substrates by a pulsed laser deposition method. From out-of-plane and in-plane X-ray diffraction measurements, the obtained ZnO films showed a single phase with the (0001) orientation on the GGG (001) and (111) substrates. The epitaxial relations between the ZnO film and GGG (001) substrate were [10-10] ZnO ‖  GGG and [10-10] ZnO ‖  GGG, while the epitaxial relations between the ZnO film and GGG (111) substrate were [10-10] ZnO ‖ [11-2] GGG ±21°. Furthermore, transmittance electron microscopy revealed sharp interfaces between ZnO films and GGG substrates. From photoluminescent spectra, the ZnO films showed donor bound emissions superimposed with free excitons at a low temperature of 10 K.