We report measurements of the cross section of the Li-8(d, alpha) He-6 reaction in the energy range E-c.m. =2.3-3.5 MeV using a Li-8-radioactive beam on a CD2 foil. The astrophysical S factor and reaction rate were calculated from the measured cross section. The He-6 nuclei produced in the reaction were detected in solidstate detector telescopes. This reaction might have affected the primordial abundance of Li-6 in big bang nucleosynthesis, since He-6 beta decays to Li-6. However, several big bang nucleosynthesis network calculations were found to be insensitive to this reaction, suggesting that the Li-8(d, alpha) He-6 reaction does not affect Li-6 primordial production.