The hydrogen storage (1-10H(2)) properties of single- and double-side lithium decorated ThMoB4-type graphene (Li/ThMoB4-C) are systematically investigated by density functional first-principles calculations within Dmol(3) package. After well-converged geometry optimizations, it is found that the binding energy of Li adatom is higher enough, and there is no adatom clustering. The average adsorption energies of 1-6 H-2 deviate in 0.20-0.27 eV/H-2 range, which is providing a convenient physical adsorption-desorption cycle. A detailed examination of the binding mechanism between the constituents of the H-2 adsorbed Li-decorated systems is presented by density of states, Mulliken charge analysis, electron density and density difference calculations. For further decoration and adsorption with 12Li adatom and 72H(2) molecules, the computation yields a high gravimetric density of 14.5 wt % with the acceptable adsorption energy. In this way, it is concluded that Li/ThMoB4 system can be considered as a promising hydrogen storage medium. (C) 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.