This report describes the growth of single-crystalline ZnO films on Si (111) substrates by plasma-assisted molecular-beam epitaxy. X-ray diffraction measurement shows that c-axis oriented ZnO films are easily grown on Si (111) substrates. However, in-plane random rotational domains are included in the ZnO films due to the inevitable oxidation of substrate surface at the initial stage of ZnO growth. By employing a thin CaF2 buffer layer between the ZnO films and Si substrates, we have succeeded in suppressing the generation of rotational domains and in obtaining an intense ultraviolet photoluminescence even at room temperature. These results indicate that the use of CaF2 buffer layer is promising for the growth of device-quality ZnO films on Si (111) substrates.