The geometric and electronic structures of the bimetallic cluster, Na6Pb, have been calculated using the density functional and coupled-cluster approaches, with a relativistic effective core potential and one-electron spin-orbit operators. Six possible isomeric Na6Pb structures (O-h, D-3h, D-3d, C-5 upsilon, C-3 upsilon, and C-2 upsilon) have been examined, and the highly symmetrical O-h structure was found to be the most stable form. The stabilities of the clusters correlate well with the Pb-Na bond distances and with the charge transfer from the Na-6 subsystem to the more electronegative Pb atom. The binding energies were found to vary according to the structure, with a spread of about 0.1 eV and 0.3 eV for the density functional and coupled-cluster calculations, respectively. These are of the same order, and somewhat smaller, as are found for the Na6Mg clusters (about 0.5 eV), demonstrating that the stabilization of the Na6Pb cluster is not particularly dependent on the geometric structures. At the same time, we found that the Na6Pb cluster is more stable as the symmetry is higher.