The phase transition of ZnS from the zincblende (ZB) structure to the rocksalt (RS) structure is investigated by the ab initio plane-wave pseudopotential density functional theory method. It is found that the pressures for transition from the ZB structure to the RS structure are 17.5 GPa from total energy–volume data and 15.4 GPa from equal enthalpies, consistent with the experimental data. From the high pressure elastic constants obtained, we find that the ZB structure ZnS is unstable when the applied pressure is larger than 17 GPa. Moreover, the dependence of the normalized primitive cell volume V/V0 on pressure P can also be successfully obtained.