The demand for clean renewable energy is urgent in current. The hydrogen application is difficult mainly due to the ratively low capacity in the storage medium. In this work, the adsorption and desorption of the hydrogen molecules by the Li atoms decorated B-38 cage are studied by the density functional theory. The calculated largest binding energy of one Li atom (2.68 eV and 2.58 eV) is upon the hexagonal hole of the B-38 cage, which is much larger than the experimental cohesive energy of bulk Li (1.63 eV). Each Li atom in the outside of the B-38 cage can adsorb up to four H-2 molecules. The E-ad of B-38(Li-nH(2))(4) decreases from the 0.22 eV for n = 1 to the 0.11 eV for n = 4. The B-38(Li-4H(2))(4) structure achieves the 6.85 wt% hydrogen gravimetric density, which is higher than the goal of 5.5 wt% before 2017 set by the United States Department of Energy. The almost the same partial density of states for the fifth H-2 molecule as that of the isolated H-2 molecule, the longer 4.5 angstrom distance between the fifth H-2 molecule and the Li atom, together with the small NBO charges all reveal the weak electronic field around the Li+, which can interpret the weak H-2 adsorption mechanism. Finally, the B38Li4 structure can easily release 9H(2) molecules at 373 K known from the molecular dynamic simulation and practically trap about 1.08H(2) molecules at 373 K/3 atom condition calculated by the grand partition function. Thus, its reversible practical HGD of B38Li4-14.34H(2) is 6.18 wt%, which is almost the same value as the theoretical 6.85 wt% for B-38(Li-4H(2))(4). Our studies will be the strong theory basis for the future application in hydrogen storage material development. (C) 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.