Using the first-principles method based on density functional theory we study the structural properties of zinc-blende structure, rocksalt structure and hexagonal wurtzite structure of ZnSe. At the same time, according to the isoenthalpy principle, we have found the transition pressure from zinc-blende to rocksalt is about 15.5 GPa, which is in good agreement with the experimental result. The elastic constants of ZnSe with zinc-blende structure under different pressures are calculated. The relationship between the thermal expansion coefficient and the pressure at different temperatures are obtained based on the quasi-harmonic Debye model.