We found that inserting a low-temperature-grown layer of GaN between a low-temperature-grown InN buffer layer and a sapphire substrate was an effective way of improving structural and electrical properties of InN films grown by plasma-assisted molecular beam epitaxy. The surface of a 260 nm thick InN film grown under the optimum condition was smooth, with a surface root-mean-square roughness of less than 4 nm. The Hall mobility of the InN film at room temperature was greater than 1500 cm2/Vs with an electron density of less than 2.0 × 1018 cm–3.