Abstract We have systematically explored the crystal structures of alkaline-earth metal sulfides under pressure by using a swarm-intelligence structural prediction method. At low pressures we successfully reproduced their known structures and phase transition sequences. Under high pressure, MgS is predicted to transform from B28 to a β-NbP-type structure at 262 GPa. CaS and SrS present the same phase transition sequence, from B2 to a β-NbP-type structure, while BaS is predicted to transform to a Imma structure. The Imma structure is actually similar to the β-NbP-type structure, as it can be seen as a modulated distortion of the latter structure. The absence of any imaginary phonon mode for the predicted structures suggests that they are dynamically stable. The calculated electronic band structures and density of states reveal that all the predicted phases are metallic, except that MgS is a semiconductor. Subsequent electron-phonon coupling calculations suggest that Imma BaS is a superconductor with a low T _c of 1.32 K, while β-NbP MgS, CaS and SrS are not superconductors. The current study provides a comprehensive analysis of phase transitions for alkaline-earth metal sulfides up to 300 GPa and might stimulate experimental studies in the future.