A series of InN films were grown on GaN-on-sapphire template with H2 pulse flow by metal organic vapor phase epitaxy. The scanning electron microscopy and atomic force microscopy observations demonstrate that the smooth surface has been achieved. The X-ray diffraction and Raman spectra measurements indicate that InN layers experience stronger accommodated compressive stress, resulting in a larger fraction of (002) oriented InN grains. On the basics of the first-principles calculations, these features can be understand as competition between N-penetrating effect with the assistance of the H atom and the etching effect of H2. Finally, the absorption spectra in conjunction with simulated results reveal that the band gap energy predominantly increase with increasing compressive strain.