The MgxZn(1-x)O alloy system may provide an optically tunable family of wide band gap materials that can be used in various UV luminescences, absorption, lighting, and display applications. A systematic investigation of the MgO-ZnO system using ab initio evolutionary simulations shows that MgxZn(1-x)O alloys exist in ordered ground-state structures at pressures above about 6.5 GPa. Detailed enthalpy calculations for the most stable structures allowed us to construct the pressure-composition phase diagram. In the entire composition, no phase transition from wurzite to rock-salt takes place with increasing Mg content. We also found two different slops occur at near x = 0.75 of Eg-x curves for different pressures, and the band gaps of high pressure ground-state MgxZn(1-x)O alloys at the Mg concentration of x > 0.75 increase more rapidly than x < 0.75.