Based on first-principles density functional theory (DFT) calculations, we systematically studied the potential application of a new two-dimensional carbon allotrope nanomaterial C568 in Lithium-ion batteries (LIBs) in this paper. Results show that the average adsorption energy of Li over fully-charged monolayer C568 is −0.25 eV, which guarantees the good stability of the C568 during the charging and discharging process. Besides, monolayer C568 exhibits a low barrier of 0.42 eV for Li diffusion. The theoretical capacity of monolayer C568 reaches up to 1373.3 mAhg−1, which is much higher than that of the most reported 2D anode materials. It was found that C568 monolayer has great potential as an attractive anode material for LIBs with the high power density and good rate capacity.