Based on density functional theory (DFT), first-principles molecular dynamics (MD), and the grand canonical ensemble Monte Carlo (GCMC) method, we investigated the boron substitution in aromatic rings of graphyne in terms of geometric and electronic structures as well as its bifunctional application including Li and H2 storage. The calculated binding energies of B-doped graphyne (BG) are significantly enhanced at two adsorptive sites compared to pristine graphyne, leading to high lithiation potentials of 2.7 V in 6Li@1BG, and even higher with 3.0 V in 6Li@3BG. Thus, 6Li@1BG with a capacity of 1125 mA h g(-1), which is much larger than other carbon materials, is proposed to be a good anode material in lithium-ion batteries. For further hydrogen storage in 6Li@nBG, the results show that it can steadily adsorb at least 8H2 in DFT, MD and GCMC computations, and the excess gravimetric H2 uptake is 7.4 wt% at ambient conditions, exceeding the 2017 DOE target. Our multiscale simulations demonstrate that chemical modifications in two-dimensional carbon structures are very promising for high lithium storage and hydrogen uptake.