GaN have sphalerite structure (Cubic-GaN) and wurtzite structure (hexagonal GaN). We report the H-GaN epilayer with a LT-AlN buffer layer has been grown on Si(1 1 1) substrate by metal-organic chemical vapor deposition (MOCVD). According to the FWHM values of 0.166° and 14.01 cm⁻¹ of HDXRD curve and E₂ (high) phonon of Raman spectrum respectively, we found that the crystal quality is perfect. And based on the XRD spectrum, the crystal lattice constants of Si (a = 5.3354 Ǻ) and H-GaN (a_epi = 3.214 Ǻ, c_epi = 5.119 Ǻ) have been calculated for researching the tetragonal distortion of the sample. These results indicate that the GaN epilayer is in tensile strain and Si substrate is in compressive strain which were good agreement with the analysis of Raman peaks shift. Comparing with typical values of screw-type (D_screw = 7 × 10⁸ cm⁻²) and edge-type (D_edge = 2.9 × 10⁹ cm⁻²) dislocation density, which is larger than that in GaN epilayers growth on SiC or sapphire substrates. But our finding is important for the understanding and application of nitride semiconductors.