Growth of GaN on 4H- or 6H-SiC (0001) Si-face substrates with various misorientation angles and directions is presented. GaN layers were directly grown on the SiC substrates by molecular-beam epitaxy using elemental Ga and rf plasma-excited active nitrogen. First, 4H-SiC (0001) 8°-off toward the [11–20] direction was investigated. Before the growth of GaN, ex-situ high-temperature gas etching was carried out, resulting in a smooth SiC initial surface. However, the surface of the subsequently grown GaN layer has wavy features with peak-to-valley height of 30 nm. Since the direction of the undulations is parallel to the misorientation direction, this feature must originate from the substrate misorientation. Step bunching and large faceting along <01–10> and <10–10> directions occurred during the growth of GaN. Lowering the growth temperature suppresses large faceting, and results in reduction of the peak-to-valley height to 3 nm. However, the surface still has the same undulating features on a smaller length scale. On the other hand such morphology was not observed for GaN grown on (0001) on-axis SiC substrates (misorientation < 0.3°). The influence of the polytype of the SiC substrate and the misorientation angle and direction are also discussed.