We have grown ZnO(0001) single-crystalline thin films on Si(001) using cubic yttria-stabilized-zirconia (c-YSZ) buffer and analyzed details of epitaxy, twins, and interfaces. In-plane epitaxial relationship between ZnO and c-YSZ showed an interesting dependence on growth temperature where it changed from (0001)[2¯110]ZnO||(001)[110]c-YSZ to (0001)[2¯110]ZnO||(001)[100]c-YSZ as the temperature increased from 500 to 750 °C. At temperatures in between, a combination of these epitaxial relationships was observed. We found that the epitaxial relationships are determined by the surface termination characteristics of c-YSZ across the ZnO/c-YSZ interface. The crystallographic characteristics of c-ZnO/c-YSZ/Si(001) heterostructures can be precisely tuned to address the needs of next-generation solid-state devices.