By means of the band calculations based on the FLAPW (full-potential linearized augmented plane-wave) method, information about the energy characteristics, the charge states of atoms, the nature of chemical bonds, the structure of the valence and conductivity bands of polymorphous modifications of magnesium dihydride is obtained. As found, all phases of magnesium dihydride are nonmagnetic insulators, and the electron states of the metal and hydrogen atoms turn out to be hybridized throughout their valence and conduction bands. As shown, the decrease in a total charge of electrons within the interatomic region leads to the decrease in cohesive energies of the high-pressure magnesium-dihydride phases that can to improve the kinetics of hydrogen desorption from them.