The utilization of hydrogen as a clean fuel has been made feasible by the expanding development of cutting-edge materials for hydrogen adsorption and storage. In this study, we thoroughly assessed hydrogen storage capability on both neutral and charge-injected graphdiyne (GDY) nanosheets modified with Al doping and Li decorating (Li.Al-GDY). According to the findings, pure GDY has an adsorption energy of −0.093 eV, while GDY modified with Al and Li atoms has an improved adsorption energy of −0.577 eV. The highest H2 adsorption energy of −0.760 eV was calculated for the applied charge of −2 e to the Li.Al-GDY nanosheet, indicating a significant enhancement in the adsorption energy with the charge injection. While the pristine GDY nanosheet serves as a very poor H2 molecule adsorber and cannot even hold one H2 molecule, the charged Li.Al-GDY nanosheet maintains 13 H2 molecules with an average adsorption energy of −0.287 eV. According to the results, injecting charge into the nanosheet along with modification techniques such as doping and decorating can significantly boost the effectiveness of weak carbon adsorbents in terms of hydrogen adsorption. Such approaches enable the realization of the goal of using carbon adsorbents as H2 green fuel storage.