The high pressure phase transition at zero temperature and the phonon-dispersion relations at zero temperatue and zero pressue of BeO have been studied by a first-principles method. The results show that a phase transition from wurtzite structure (B4) to cubic sodium chloride structure (B1) happens at about 122 GPa and the zinc blende phase (B3) is of a meta-stable structure at zero temperature and zero pressure. The phonon-dispersion relations of B1, B3 and B4 phase BeO at zero temperature and zero pressure are investigated by the frozen phonon method. The calculations show that at zero temperature and zero pressure B1 phase is an unstable phase and B4 and B3 phases are of two very simliar structure, but they are still distinguishable from each other by their phonon-dispersion relations. Finally, the phase diagrams of BeO at high temperature and high pressure are studied.