Calculations of the electronic structure and the density of states of GaN with Mn are carried out by means of first-principles plane-wave pesudopotential method based on density functional theory. The results reveal a 100% spin polarized impurity band in band structure of Ga1-xMnxN due to hybridization of Mn 3d and N 2p orbitals. The material is half metallic and suited for spin injectors. In addition, a peak of refractive index can be observed near the energy gap. The absorption coefficient increases in the UV region with the increase of the Mn content.