It is known that low-dimensional carbon allotropes can be used as a new class of anode materials for lithium-ion batteries. However, the existing carbon allotropes cannot meet the increasing energy and power demand, and thus there is still a need for further development of new materials for lithium-ion batteries. In the present work, a new graphene allotrope, known as graphenylene, is found to be capable of storing lithium with greater density of energy. Ab initio density functional theory calculations indicate that the unique dodecagonal holes in graphenylene enable lithium ions to diffuse both on and through graphenylene layers with energy barriers no higher than 0.99 eV. Adsorption of a lithium atom on graphenylene is stronger than that on pristine graphene. The highest lithium storage capacities for monolayer and bilayer graphenylene compounds are Li₃C₆ and Li_2.5C₆, respectively, which correspond to specific capacities of 1116 and 930 mA h g⁻¹. Both specific and volumetric capacities of lithium-intercalated graphenylene compounds are significantly larger than those for graphene. The high lithium mobility and large lithium storage capacity demonstrate that graphenylene is a promising anode material for modern lithium-ion batteries.