Using the first-principle pseudopotential plane wave (PPW) method based on the density functional theory, structural optimization was conducted on various intermetallic compounds of the binary Mg-Nd alloy. With their ground-state energies obtained, the structural stabilities of these intermetallic compounds were studied in terms of formation heat and binding energy of the alloy. The results show that the absolute values of the binding energies of various intermetallic compounds increase with the increase of Nd content, among which the absolute value of the binding energy of MgNd is the greatest while that of Mg12Nd is the smallest. It is indicated that among all the intermetallic compounds formed in Mg-Nd, the structure of MgNd is the most stable while that of Mg12Nd is the most unstable. This result is consistent with the experiment data. The Mg12Nd phase does not exist in the phase diagram of Mg-Nd alloy. In addition, the densities of electronic state of these structures were calculated and an explanation was given in terms of the electronic structure.