Possible geometrical structures and relative stability of MgmBn(m=1,2;n=1—4) clusters are studied by using the hybrid density functional theory(B3LYP) with 6-31G basis sets. For the most stable isomers of MgmBn(m=1,2;n=1—4) clusters, the electronic structure, vibrational properties, bond properties, ionization potential, polarizability and hyperpolarizability are analyzed. The calculated results show that most of the optimized MgmBn(m=1,2;n=1—4) clusters have planar structure, the B-B and B-Mg bonds are coexisting in the cluster, but the Mg-Mg bonds are infrequent in the clusters. The bond length of B-B is about 0.153—0.182nm and that of Mg-B is 0.221—0.231nm. The outcome of population analysis suggests that there is an electronegative center in the cluster, the other B and Mg atoms with positive charge are located at apexes of the cluster.