The measurement of the Be-7(d,He-3)Li-6* transfer cross section at 5 MeV/u is carried out. The population of the 2.186 MeV excited state of Li-6 in this reaction channel is observed for the first time. The experimental angular distributions have been analyzed in the finite range DWBA and coupled-channel frameworks. The effect of the Be-7(d,He-3)Li-6 reaction on both the Li-6 and Li-7 abundances are investigated at the relevant big-bang nucleosynthesis energies. The excitation function is calculated by TALYS and normalized to the experimental data. The S factor of the (d,He-3) channel from the present work is about 50% lower than existing data at nearby energies. At big-bang energies, the S factor is about three orders of magnitude smaller than that of the (d, p) channel. The (d,He-3) reaction rate is found to have a less than 0.1% effect on the Li-6,Li-7 abundances.