The surface morphology of GaN thin films grown by molecular beam epitaxy on nominal flat and vicinal 6H-SiC(0001) substrates was characterized by in situ scanning tunneling microscopy. On flat substrates, screw dislocations emerge at the surface, creating straight steps along the h11 2 20i direction for 50 nm film thickness. As growth proceeds, these steps wind around the dislocations and form spirals for film thickness of about 100 nm. In contrast, the spiral growth is completely suppressed on vicinal substrates, and step-flow growth was observed. Based on the Burton, Cabrera, and Frank theory, a model is proposed to explain the suppression of the spiral growth on vicinal substrates.