First-principles calculations have been used to investigate hydrogen adsorption on alkali atom doped B 36 N 36 clusters. The alkali atom adsorption takes place near the six tetragonal bridge sites available on the cage, thereby avoiding the notorious clustering problem. Adsorption of alkali atoms involves a charge transfer process, creating positively charged alkali atoms and this polarizes the H 2 molecules thereby, increasing their binding energy. Li atom has been found to adsorb up to three hydrogen molecules with an average binding energy of 0.189eV. The fully doped Li 6 B 36 N 36 cluster has been found to hold up to 18 hydrogen molecules with the average binding energy of 0.146eV. This corresponds to a gravimetric density of hydrogen storage of 3.7wt.%. Chemisorption on the Li 6 B 36 N 36 has been found to be an exothermic reaction, in which 60 hydrogen atoms chemisorbed with an average chemisorption energy of −2.13eV. Thus, the maximum hydrogen storage capacity of Li doped BN fullerene is 8.9wt.% in which 60 hydrogen atoms were chemisorbed and 12 hydrogen molecules were adsorbed in molecular form.