InN films were grown on Si (111) substrates by radio-frequency plasma-excited molecular beam epitaxy. InN films highly oriented to the c-axis were obtained by optimizing growth conditions in the direct growth on Si. Growth of single crystalline InN films was realized on Si substrates with substrate nitridation for 3 min. On the other hands, when the substrate nitridation was lasted over 30 min, obtained InN films were polycrystalline due to the amorphous SiNx layer formed on a substrate surface. We also studied the local atomic structure in the single crystalline InN film using extended X-ray absorption fine structure measurements.