The equations of state and phase transition of ZnTe in zinc blende (ZB) and cinnabar (CB) structures under high pressure are investigated by the projected augmented wave method in the scheme of density functional theory. The primitive cell volumes, electronic structures and optical properties are also predicted before and after phase transition. The variations of the calculated total energy with volume, for the structures of ZB and CB, yield the information about the static equation of state and phase stability. The results show that the ZB phase of ZnTe has lower energy, and is more stable than its CB phase. The pressure-induced transition occurs along the common tangent line connecting the tangential points on the two enthalpy-volume curves. The calculations show that the phase transition pressure is 8.6 GPa from the ZB structure to the CB structure. The value is also compatible with those of other available theoretical and experimental results. Just before the ZB phase is transferred to the CB phase at about 8.6 GPa, the volume is reduced by 13.0% relative to the former volume at the ambient pressure condition. The calculated critical volumes and volume compressibilities by using two methods agree well with other results in the literature. The lattice parameters and equations of state of the two structures are also obtained. Metallization case of other similar materials such as ZnS caused by high pressure does not occur here. The CB phase has the behavior of indirect band gap with 0.98 eV along the symmetry of GK. After phase transition, the distributions of density of states of Zn and Te atoms of the CB structure shift towards lower energy, especially in the conduction band bottom, and the band gap decreases. Energy level overlapping is more obvious in the CB structure, and orbital hybridizations still exist, that is the reason why it is the stable phase under high pressure condition. Stronger orbital hybridization helps the transitions between Te 5p and Zn 3d electrons. The main peak of imaginary part of dielectric constant is enhanced apparently with abnormal red shift, while other two peaks disappear at the same time. Macroscopic dielectric constant of ZB structure decreases as pressure increases. For CB structure, the macroscopic dielectric constant with 13.60 eV is not affected by pressure. The results provide a theoretical basis for the polarization research of ZnTe material in static electric field under high pressure.