The structural stability and electronic-structure of icosahedral La-13, La-13(-1), and La-13(+1) clusters have been studied by DMOL cluster method based on density-functional theory. The ground state of all-electron with relativity results is shown to be a distorted D-2h icosahedron by the Jahn-Teller effect. However, the binding energies of D-3d and D-5d are very close to that of the D-2h structure for La-13, La-13(-1), and La-13(+1) clusters. The effective core potential results show that the true ground state is D-5d structure. The clusters have small magnetic moments and the symmetry of cluster is an important factor in determining the magnetic moments of the clusters. The effects of interatomic spacing and coordination on atomic magnetic moment are discussed. Further, 5d electrons dominate the hybrid orbitals below the Fermi level in the neutral cluster and contribute the main spin of clusters. (C) 2004 American Institute of Physics.