In this paper, we present a theoretical study of structural, elastic and electronic properties for zinc-blende GaN using the full-potential augmented plane wave plus local orbitals (FP-APW+LO) method. The equilibrium lattice constants, the bulk modulus, the full set of cubic elastic constants as well as internal strain parameter are determined. The strain-induced changes at the low pressures in the band structure are determined for small strains. They are also expressed in terms of deformation potentials for the Γ, L, and X eigenvalues of zinc-blende structure near the band gap. The study of the pressure effect on ionicity factor is very helpful to understand the charge transfer and bonding character of GaN.