GaN layers were grown directly on the (0001)6H-SiC substrate using metalorganic molecular beam epitaxy (MO-MBE). The direct growth of GaN is important for realizing a UV laser with a substrate-side contact. Thermally heated ammonia and triethylgallium were used as sources for the GaN growth. Streak lines were observed in RHEED patterns of GaN layers, which have flat surface morphologies observed by SEM. These results indicated that the two-dimensional growth of GaN was successfully completed in the absence of a buffer layer such as AlN. The GaN layers grown at high temperatures (650 - 740 degrees C) show mixed hexagonal and cubic types of crystalline structure.