In the framework of density functional theory, the static-lattice equation of state and structural phase stability of gold have been calculated to 2 TPa by using the augmented plane wave plus local orbital method with two distinct exchange-correlation energies; corresponding to the generalized gradient approximation (GGA) and the local density approximation (LDA), respectively. The fcc structure is predicted to be the most stable phase at zero pressure, transforming to the hcp structure at 380GPa (GGA) or 490GPa (LDA), and the hcp structure transforming to the bcc structure at 1250GPa (GGA) or 790GPa (LDA), which then remains stable to up 2 TPa. The possible reasons of the phase-transition are analyzed from the electronic density of state at the different phases and volumes. The equation of state at T=0K is also given based on the calculated structural result.