The ab-initio density-functional theory (DFT) within both the Local Density Approximation (LDA) and the Generalized Gradient Approximation (GGA) is performed to study the electronic properties and the structural phase transitions of Gallium nitride (GaN) with wurtzite (WZ), zinc-blende (ZB), rocksalt (RS) and cmcm structures under pressure in the range of 0 to 100 GPa. The calculations show that the lattice parameters, the band structures and the partial density of states (PDOS) of these phases are in good agreement with the other experimental and theoretical data. In addition, we found that both the ZB and WZ structures are stable phases at ambient pressure. The structural phase transitions of GaN under high pressure are in the sequence WZ, ZB -> RS phases. The cmcm phase has not been reported before. This could be a new phase for GaN.