B-spline basis is successfully applied in this study towards the Schrodinger equation of one-electron diatomic molecules in spheroidal coordinates. 14-figure accuracy was obtained for the eigen-energies of the lowest states of H-2(+) and HeH2+. Those results were compared with the best published results. The quadrupole moments of H-2(+) were also calculated by the eigenfunctions along with 13-figure accuracy having been achieved.