The band structures of wurtzite GaN (α-GaN) are studied using the nearest and second-nearest neighbour semi-empirical tight-binding method in sp³s* model. The calculated direct fundamental gap of α-GaN is 3.45 eV, which is in good agreement with the experimental data. The density of states and the imaginary part of dielectric function (ϵ₂ (ω)) are evaluated to be in the regions - 10.0 -12 eV and 0.0 - 10.0 eV, respectively. There are mainly three peaks at 6.4, 7.5, 8.4 eV, dominating the ϵ₂ (ω) spectrum. The two components of the ϵ₂ (ω) (i.e. ϵ_2xy (ω)) and ϵ_2x (ω)) are also calculated; and the real part of dielectric function, reflectivity, absorption coefficient, and refractive index are all studied.