FP-LAPW and pseudopotential approaches have been used to investigate the structural phase transformations of GaN under high-pressure. In these calculations the local density and generalized gradient approximations (LDA and GGA) for the exchange-correlation potential have been used. Moreover, the electronic structure of the wurtzite (WZ), rocksalt (RS) and zinc-blende (ZB) phases of GaN have been calculated. The GGA result for the transition pressure of the WZ→RS transition is of 42.3 GPa, which is in very good agreement with the X-ray absorption spectroscopy value of 47 GPa. The gradient corrections to the LDA, included via GGA, have small, but not negligible, effects on the properties studied. RS-GaN is predicted to be an indirect-band-gap semiconductor, with a band-gap of 1.7 eV.