Thin films of InSb have been grown on insulating GaAs substrates using the metalorganic chemical vapor deposition technique with trimethyl indium and trimethyl antimony as reactants. We find that the mobilities obtained are usually low unless indium is predeposited onto the substrate. This indium predeposition technique greatly improves the yield of InSb films with mobilities of -50000 cm2 V-1 s-1 at room temperature and a typical thickness of 2 microns. With this predeposition technique, the electron mobilities of these films become relatively independent of the vapor stoichiometry during growth and of the growth temperature. The electron mobilities are also very uniform across a wafer. These properties are obtained even when the film growth rate exceeds 2 μm/h.