Perfect GaN or Mn-doped GaN semiconductors are widely interesting systems for optoelectronics or spintronics applications. We have investigated the structural, electronic magnetic and optical properties of perfect GaN and Mn-doped GaN in cubic structure using a supercell of 64 atoms. First principles calculations based on density functional theory are performing by using the full potential linearized augmented plane wave method. The local spin density approximation (LSDA) were used as the exchange correlation potential to calculate the structural and electronic properties. In addition, the Tran-Blaha modified Becke-Johonson (TB-mBJ) was applied to give a better description of the band gap energies, magnetic moments and optical spectra. The results show that the system of Mn-doped GaN exhibits typical half-metallic properties in which Mn forms deep levels in the forbidden band and increases static dielectric constant. The total magnetic moment is mainly from the Mn atoms and the contributions from Ga and N are very small.