The growth of high quality CdTe epitaxial films on p-InSb(111) by a simple method of temperature gradient vapor transport deposition was carried out to investigate the possibility of the existence of a two-dimensional electron gas with high mobility at CdTe/InSb heterointerfaces. From the x-ray diffraction analysis, the grown layer was found to be a CdTe epitaxial film. Photoluminescence measurements at 15 K showed that a CdTe film grown on InSb(111) in the temperature range between 180 and 280-degrees-C appeared to have an optimum crystal perfection at a substrate temperature of about 245-degrees-C. These results also indicated that the CdTe films grown above 245-degrees-C contained a significant problem due to interdiffusion from the InSb substrates during the growth.