An ab initio constant pressure study is carried out to explore the behaviour of cadmium sulfide (CdS) under high hydrostatic pressure. We have studied the structural properties of CdS using density functional theory (DFT) under pressure up to 200 GPa. CdS crystallizes in a wurtzite (WZ)-type structure under ambient conditions. CdS undergoes a structural phase transition from the hexagonal WZ-type structure with space group P63mc to cubic NaCl-type structure with space group Fm<(3)overbar>m. Another phase transition is obtained from NaCl-type structure to the orthorhombic CdS-III-type structure with space group Pmmn. The first transformation proceeds via seven intermediate states with space group Cmc2(1), P2(1), Pmn2(1), P2(1)/m, Pmmn, I4/mmm, and Cmcm. The latter transformation is based on two intermediate states with space groups Immm and P2(1)/m. These phase transitions are also studied by total energy and enthalpy calculations. According to these calculations, the phase transformations occur at about 3 and 51 GPa, respectively. Calculation results on the other basic properties, such as lattice constant, volume, and bulk modulus are also compared with those of other recent theoretical and experimental data, and generally, good agreement with the available data are obtained.