The structures and the hydrogen storage capacities of the B6 clusters and the lithium decorated B6 clusters are investigated by using the density functional theory. The results show that the hydrogen is adsorbed in the atomic form by chemical bonds in the three possible structures of the B6 cluster. The lithium atoms do not cluster on the surface of decorated B6 cluster. Every lithium atom, as hydrogen molecules are adsorbed on the surface of lithium atoms decorated B6 clusters, can adsorb several intact hydrogen molecules. Of the lithium decorated B6 clusters the B6 cage cluster which is decorated by two lithium atoms can most adsorb the intact hydrogen molecules. The calculated gravimetric density and the average adsorption energy of hydrogen molecule are 20.38% and 1.683 kcal/mol, respectively, which are suitable for reversible hydrogen storage under the ambient condition of the normal temperature and pressure.