Structural and electronic properties of clean polar ZnO surfaces are studied by using the first-principles ultra-soft pseudo-potential approach to the plane wave, based on the density functional theory. Furthermore, the relaxations, bandstructures, and densities of states for ZnO(0001) and ZnO(0001) surfaces and the N adsorption for ZnO(0001) surface are studied. The calculation results reveal that the relaxation of ZnO(0001) surface is stronger than that of ZnO(0001) surface, so ZnO(0001) surface has a better integrity. Compared with the ZnO bulk, the ZnO(0001) surface has a narrow bandgap, and big conductivity due to the delocalizing characters. However, the bandgap of the ZnO(0001) surface widens, the empty energy levels appear near the top of bandgap due to the existence of O-2p states, and the body electrons transite easily to the surface, under the thermal excitation, and resulting in negative charges.We find that the face-centered site is the stablest adsorption position of ZnO (0001) surface, and the formation energy is lowest in the first layer when N atoms are embeded in the ZnO (0001) surface. Therefore, N atoms easily accumulate on the surface layer rather than occupy the positions in the body.