The heteroepitaxial growth of a GaN single crystal by metal-organic vapor phase epitaxy on a 4H-SiC (3038) substrate was demonstrated. The crystallographic orientation of GaN was found to be dependent on growth pressure. When the growth pressure was 1000 hPa, the orientation of the GaN single crystal was consistent with that of the SiC substrate, where the c-plane of the GaN was single crystal tilted 54.7° from the surface plane. Then, we fabricated a violet-light-emitting diode (LED) with a GaInN multiple-quantum-well (QW) active layer grown on the GaN layer, which coherently grew on the 4H-SiC (3038 ) substrate. The blue shift of the peak wavelength with increasing injection current of up to 100 mA was confirmed to be two times smaller than that of a conventional LED on a c-plane sapphire substrate due to a low internal polarization.