To design the high-energy-density Li-ion batteries, the anode materials with high specific capacity have attracted much attention. In this work, we adopt the first principles calculations to investigate the possibility of a new two dimensional boron material, named BG, as anode material for Li-ion batteries. The calculated results show that the maximum theoretical specific capacity of BG is 1653 mAh g−1 (LiB1.5). Additionally, the energy barriers of Li ion and Li vacancy diffusion are 330 meV and 110 meV, respectively, which imply fast charge and discharge ability for BG as an anode material. The theoretical findings reported in this work suggest that BG is a potential candidate as anode material of high-energy-density Li-ion batteries.