The Saturn-like charge-transfer complex Li4&B36, which was recently predicted with extensive first-principles theory calculations, were studied as a candidate for hydrogen storage material in the present work. The bonding characters of Li-B, B-B and Li-H2 bonds were revealed by the quantum theory of atoms in molecules (QTAIM). Each Li atom in Li4&B36 cluster can bind six H2 molecules at most, which results into the gravimetric density of 10.4%. The adsorption energies of H2 molecules on Li4&B36 cluster are predicted in the range of 0.08-0.14 eV at the wB97x level of theory.