We have systematically studied the structural and electronic properties of MgS crystal by means of accurate first principle calculations. Our results show that this crystal has indirect band gap in the B1 structure and direct band gap in the B2,B3 and the B4 structures. Energy band width of the B2 structure is the smallest. When the pressure is below 200.3GPa, the B1 structure of MgS crystal is most stable. Above 200.3GPa this compound would undergo a structural phase transition from the relatively loose NaCl structure to the more dense CsCl atomic arrangement.