The electronic structure and optical properties of pure and Al_and Mg-doped cubic-blende GaN have been studied based on the density functional theory and the generalized gradient approximation method. The relationship between the distribution of the electronic states and their structures has been analyzed.The dielectric function and the complex refractive index function on the doping GaN system have been obtained. The calculation results indicate that the hole concentration of Mg-doped GaN is increased and the Mg-doping markedly enhanced the conductivity of the material.But the carrier concentration of Al-doped GaN is not changed and optical bandgap is broadened.The mechanism of luminescence has been explained in terms of an analysis of the dielectric function and the complex refractive index function. It offers theoretical data for the design and application of GaN optoelectronic materials. By comparison, our results are in good agreement with that published in the literatures.