Epitaxial growth of GaN has been tried using various kinds of substrates so far. Of all the substrate, Al2O3 has been widely used for the GaN growth. Besides Al2O3, SiC is also expected as one of the most suitable substrates for the GaN growth, since SiC has a small mismatch in the lattice parameters with GaN and has good thermal stability under controlled atmospheres during the GaN growth. Both 6H-SiC and GaN having wurtzite structure belong to the same space group (P6(3)mc). The lattice parameters are as follows : a=3.08, c=15.08Angstrom for 6H-SiC and a=3.19, c=5.18Angstrom for GaN. SiC has two opposite surface polarities along [001] direction. The main objective of our research was to establish a crystallographic growth model of GaN on the (00(.)1)6H-SiC with different polarities of Si and C surfaces.