The wavelength-dependent and frequency-dependent dielectric function of wurtzite-GaN is calculated totally from fundamental parameters such as the lattice constant using Walter’s ab initio model.The errors occurring in the calculation are carefully reduced by linear interpolation of energy data.The Kramers-Kr(o)nig transform of the real part of greater range is obtained by extrapolation of the real part.The calculation is time-consuming but meaningful.The long-wave results are similar to the experimental data of the photon and are useful for related investigation of properties of wide-gap semiconductors such as electron scattering like the Auger recombination and impact ionization.