Ab-initio total energy calculations have been performed utilizing the Density Functional Theory (DFT) inside the generalized gradient approximation (GGA) parameterized by Perdew-Burke-Ernzerhof (PBE). Interactions of the ions and electrons with each other’s was characterized via PAW potential within the valance electron configurations Ga-4s24p1 and N-2p22p3 to investigate the physical properties in the rocksalt B1 and wurtzite B4 phases. The equilibrium transition pressure (Pt) from B4 to B1 was estimated at about 33.66 GPa by using the common tangent construction. The DFT calculations indicate that the upper bands of wurtzite B4 between -0.256 eV and the Fermi level were mostly owing to N-p states. The lowest conduction bands were consisted of a mixture of N-s and Ga-s states. The valance band maximum and the conduction band minimum occured at the Γ symmetry point. Concordantly, B4 phase of GaN had a direct band gap at Γ-point, which calculated as 1.702 eV. The highest valance band of rocksalt B1 were consisted of with a major contribution of N-2p states. Although, the indirect band gap of the rocksalt B1 phase has been reported from the valance band maximum at the L-point to the conduction band minimum along the X direction [7], we observed the indirect energy band gap from the valance band maximum at the L-point to the conduction band minimum along the Γ direction. Our calculated value of indirect energy band gap for the rocksalt B1 phase was 0.777 eV and it was lower than the previous calculations.