We present a first-principle study of the vibrational and thermodynamic properties of Mg2Si04 forsterite up to 20 GPa. The calculated local density approximation (LDA) frequencies and their pressure dependence are in good agreement with the available Raman and infrared spectroscopy data. We also predict the pressure dependence of the modes which are yet to be measured. Thermodynamic properties are obtained using the quasi-harmonic approximation (QHA) to the free energy in conjunction with these results. The calculated pressure-volume-temperature (P-V-T) relations and thermodynamic properties agree well with the reported experimental data within the regime of validity of the QHA. The only discrepancies with experimental data that point to intrinsic anharmonic effects are the mode Gruneisen parameters of two Raman and one infrared modes. However, their effect on thermodynamic properties appears to be negligible.