We report the results of a theoretical study on the behaviour of the structural parameters and the pressure of transitions from B4 (wurtzite) to B3 (zinc-blende) phase, from B4 (wurtzite) to B1 (rocksalt) phase and from B3 (zinc-blende) to B1 (rocksalt) phase of GaN in a significant range of pressure from 0 to 100 GPa at T = 0 K. According to our knowledge, for the first time a theoretical study is driven until 100 GPa. The transition from B4 (wurtzite) to B3 (zinc-blende) phase is not reported in literature. For this reason the pressure of transition and the evolution of the structural parameters are estimated according to the corresponding pressure. The calculations are based on the ab initio plane-wave pseudo-potential Density-Functional Theory (DFT), within both the Generalized Gradient Approximation (GGA) and Local-Density Approximation (LDA) for the exchange and correlation potential. The calculated values of transition pressure, lattice parameters are in very good agreement with experimental results. A linearresponse approach to the density-functional theory is used to derive the phonon frequencies and densities of states. Where, we discussed the contribution of the phonons in the instability of B3 (zinc-blende) phase.