Self-consistent minimum free-energy calculations of the structure and lattice dynamics of forsterite at high pressure (up to 30 GPa) and high temperature (up to 1850 K) have been performed using an approach based on the Born model of solids. In the free-energy minimization procedure, lattice dynamics and thermodynamic properties are calculated self-consistently within the quasi-harmonic approximation (QHA). The results of the free-energy minimizations am compared with recent spectroscopic studies of forsterite at high pressure and high temperature. The predicted variations of mode frequencies with compression am consistent with those obtained from high-pressure spectroscopy. On the other hand, the variations with temperature am underestimated. Because the variations of lattice dynamics with pressure are related to anharmonic properties such as the Gruneisen parameter and thermal expansion, it is concluded that most of the extrinsic (i.e., volume dependent) anharmonicity can be accounted for within the QHA. On the other hand, the variations of the lattice dynamics with temperature also include intrinsic (i.e., volume free) anharmonic effects, which are not accounted for in the QHA. In forsterite, these effects become significant for thermodynamic properties (heat capacities and thermal expansion) above 1200 K.