The structural, elastic, electronic and optical properties of MgS B2 crystal under high pressure are studied by accurate first-principles plane wave pseudo-potential method which is based on the density functional theory. Our results show that the conduction band of the structure has a shift tendency toward higher energy, and the valence band has a shift tendency toward lower energy under high pressure. We analyze the optical properties associated with the partial density of states and the shift of energy level under high pressure. At the same time, the absorption spectrum of the MgS B2 crystal has an evident blue shift.