The phase transitions and structure stabilities of materials have always attracted much attention of the experimental and theoretical investigators. When calculating the phonon dispersion of the cubic structure of the transition metal Zr (β -Zr), the traditional methods always give the negative phonon frequencies. So the quasi-harmonic approximation cannot solve this kind of problem. We obtain the phonon dispersion of β -Zr at high pressure and high temperature by using the newly developed self-consistent ab initio lattice dynamics method, which can well consider the phonon-phonon interactions. And then the stable region of β -Zr in the high pressure and high temperature phase diagram is predicted. The full phase diagram of Zr is also predicted. We also obtain the high temperature equation of state (EOS) and thermal expansion of β -Zr, which can help to construct the EOS data base of Zr.