Holey graphyne (HGY), a novel two-dimensional (2D) single-crystalline carbon allotrope, was recently synthesized by Castro-Stephens coupling reaction. The naturally existing uniform periodic holes in the 2D carbon-carbon network demonstrate its promising potential in energy storage. Herein, we conduct density functional theory (DFT) calculation and ab initio molecular dynamics simulations (AIMD) to predict the H storage properties of a single-layer HGY sheet modified by Li metal atoms. The DFT calculations demonstrate that Li atoms can bind strongly to the HGY sheet without forming clusters, and each Li atom can anchor four H2 molecules with an average adsorption energy of about -0.22 eV/H2. The largest H storage capacity of the doped HGY sheet can reach as high as 12.8 wt%, showing that the Li/HGY complex is an ideal H storage material at ambient conditions. In addition, we investigate the polarization mechanism of the storage media and find that the polarization originates from the electric field induced by both the ionic Li atoms and the weak polarized H2 molecules. Finally, the desorption mechanism of the adsorbed H2 molecules is thoroughly investigated using a kinetic AIMD method.