Adsorption of Li, Na, and K atom on surfaces of armchair (5,5) and zigzag (10,0) hydrogen boride nanotubes (HBNTs) was investigated using the periodic-DFT method. It was found that the average diameter (5,5) HBNT is shorter than the (10,0) HBNT by 1.246 Å and the (5,5) HBNT is more stable than the (10,0) HBNT by 0.991 eV. Adsorption strength of the (5,5) HBNT on alkali metals was found to be higher than the (10,0) HBNT. Adsorption abilities of H2 on the (5,5) HBNT and (5,5) HBNT are in the same order: Li > Na > K. The adsorption energies of H2 on Li-, Na-, and K-(5,5) HBNTs are −0.242, −0.165, and −0.121 eV, respectively, and on Li-, Na-, and K-(10,0) HBNTs are −0.277, −0.168, and −0.094 eV, respectively. The Li-HBNTs, Li-(5,5) HBNT, and (10,0) HBNT are the highest adsorption abilities on H2 adsorption and the most significant change of metal charges. Therefore, the Li-(5,5) HBNT and (10,0) HBNT used as H2 storage materials were suggested.