A systematic first-principles investigation, by using the density functional formalism with the nonlocal B3LYP approximation including a long-range dispersion correction, has been performed to calculate the structural and electronic properties and phase transitions under pressure of the three phases of ZnS (cubic zinc blende, ZB, hexagonal wurtzite, W, and cubic rock salt, RS). Numerical and analytical fittings have been carried out to determine the equilibrium unit cell geometry and equation of state parameters for the ZnS phases. The band structures, energy gap, density of states, and vibrational frequencies and their pressure dependences are investigated. The present results illustrate that both phases, W and ZB, present very similar enthalpy and the RS phase becomes thermodynamically more stable than ZB and W structures at 15.0 and 15.5GPa, respectively. These phase transitions are accompanied by an increase of the first shell coordination number of Zn atom and by a cell volume collapse of 13.9% and 14.3% for ZB and W phases, respectively. The atomic contributions of the conduction and valence bands, as well the binding energy for the Zn 3d orbital have been obtained.