The structural stabilities and electronic structures of Mg17Al12, Al2Ca, Al2Nd and Al2Er intermetallic compounds have been investigated by Castep module based on the density functional theory. The heats of formation, cohesive energies and densities of states (DOS) of these compounds are calculated and the crystal structures are optimized. Results show that the heats of formation and cohesive energies are all negative. The Al2Er has the strongest alloying ability and structural stability, then Al2Nd, thirdly Al2Ca and finally Mg17Al12. The calculated DOS of all the compounds in this study shows that Al2Er and Al2Nd exhibit the stronger structural stabilities and the reason can be deduced as follows: (1) The valence electrons between Al (3p) and Er (4f), Al (3p) and Er (5d), Al (3p) and Nd (4f), Al (3p) and Nd (5d) orbits hybrid seriously in the lower energy region below Fermi level. (2) The bonding electron numbers of Al2Nd and Al2Er are more than Al2Ca and Mg17Al12. (3) The bonding abilities of Al2Nd and Al2Er are stronger. Moreover, the calculations of density of charge indicate that all of these compounds contain metallic, ionic and covalent bonds. In these compounds, Al2Er and Al2Nd have the stronger covalent bonds than Al2Ca and Mg17Al12, while the Al2Ca has the strongest ionic bonds and the Mg17Al12 is dominated by the metallic bond.