Epitaxial pseudo cubic yttrium-stabilized Y0.05Hf0.95O2 (YHO) thin films with bottom electrode layers of Pr0.5Sr0.5CoO3 were deposited on (001)-oriented LaAlO3 (LAO) substrates by using the pulsed laser deposition system. The crystal structure and thickness of the films were confirmed by θ–2θ scan and X-ray reflectivity via X-ray diffraction technology, respectively. Reciprocal space mapping (RSM) was performed to clarify the microstructure of the epitaxial YHO films affected by LAO substrates, and the result of symmetric RSMs revealed that the crystal mosaicity of the YHO films increases with the increasing film thicknesses. Moreover, the dominant conduction mechanisms of all the YHO films were ohmic conduction in the low electric field. At a high applied electric field, the YHO-5.4 nm film was determined by the space-charge-limited current behavior, while the samples of the YHO-9.8 nm and YHO-19.2 nm films were determined by ohmic conduction. The temperature-dependent I–V characteristics of the YHO films with different thicknesses have been also obtained, revealing that the current of all the YHO films generally increases with the increase in temperature, which attributed to the crystal mosaicity and chemical defects.