Motivated by novel graphyne-like carbon nanostructure C68-GY, spin-polarized DFT calculations with dispersion-correction were performed to investigate the hydrogen adsorption capacity of Li decorated C68-GY nanosheet. The binding energy between Li and C68-GY was larger than the cohesive energy of bulk metal, indicating Li atoms would prefer to separately attached on C68-GY. The ab initio molecular dynamics simulation has been performed to confirm the stability of Li/C complex. When five Li atoms decorated on C68-GY, 14H2 molecules were captured. The maximum hydrogen storage density was 8.04 wt% with an average hydrogen adsorption energy of −0.227 eV per H2. The positively charged Li atoms aroused electrostatic field and induced the polarization of H2. It was notable to observe strong hybridization between the main peak of H-1s orbitals with Li below Fermi level, which was responsible for the enhancement of hydrogen binding energy, indicating its potential application on hydrogen storage.