The band structure, the density of states, the surface energy, the work function, and the optical properties of GaN(0001)(22) clean surface are calculated systematically by the first-principles plane-wave ultro-soft pseudopotential method based on the density function theory. It is found that the band structure of GaN(0001) surface changes greatly after relaxation, the surface has metallic conductive properties, and there is obvious surface state near the bottom of conduction band. In the effect of dipole moment, the surface charges shift and Ga-terminated surface is positive polar surface. the surface energy and the work function of GaN (0001) surface are obtained to be 2.1 J.m-2 and 4.2 eV, respectively. The optical properties of GaN (0001) surface and bulk phase GaN are analyzed and compared. It is found that there is big difference between them.