The band structure, density of states and optical properties of zinc-blende GaN are calculated systematically by using the first-principles plane-wave pseudopotential method, based on the density function theory. Results show that zinc-blende GaN is a typical direct band gap semiconductor. The band gap is 1.496eV, the valence bands are attributed to Ga3d, N2s and N2p electronic states, and the conduction bands are attributed to Ga4s and Ga4p electronic states. The electrical transport properties and types of carriers of GaN are attributed to N2p and Ga4s electronic states near the Fermi level. The static dielectric constant ɛ 1 (0)=3.9065eV, the refractive index n0=1.9765 eV, and the maximum peak of absorption coefficient is 354655.6cm −1 . The dielectric function, refractive index, absorption spectra, reflective spectra, optical conductivity and energy loss function are calculated using band structure and density of states. This provides a theoretical basis for the design and application of GaN opto-electronic materials.