The total energy and strength of Mg alloy doped with Al, Ca and Zn, were calculated using thedensity functional theory. The calculations was performed by two programs; the discrete variational Xα (DV-Xα) method, which is a sort of molecular orbital full potential method; Vienna Ab-initio Simulation Package(VASP), which is a sort of pseudo potential method. The fundamental mixed orbital structure in each energylevel near the Fermi level was investigated with simple model using DV-Xα. The optimized crystal structurescalculated by VASP were compared to the measured structure. The density of state and the energy levels ofdopant elements was discussed in association with properties. When the lattice parameter obtained from thisstudy was compared, it was slightly different from the theoretical value but it was similar to Mk, and weobtained the reliability of data. A parameter Mk obtained by the DV-Xα method was proportional toelectronegativity and inversely proportional to ionic radii. We can predict the mechanical properties becauseis proportional to hardness.