In recent years, the use and storage of hydrogen has attracted more and more attention as environmental and energy issues become more prominent. In this paper, we propose a solution to store hydrogen using a recently discovered graphene allotrope called Me-graphene, which needs to be doped with nitrogen and decorated with lithium. First-principles were used to explore evaluation results. We assumed three models, each doped with an N atom at a different location, and then discussed their electronic structures. Because metal ions help to enhance the absorption of hydrogen, we tested the adsorption capacity of Li at different positions on the upper and lower surfaces of the three structures, and finally found the most stable adsorption sites of Li. On this basis, the adsorption capacity of hydrogen molecules was discussed. It was found that for N doping at three different points, the maximum adsorption number of hydrogen molecules was 8, 5, and 8, and their corresponding gravimetric density were 8.57, 5.54, and 8.57 wt% respectively. Therefore, our study contributes to the potential application of Li decorated N-doped Me-graphene in the field of reversible solid-state hydrogen molecule storage materials.