Abstract Density functional theory investigations show that the Li + ion is stabilized at the center of hexagonal carbon ring with the distance of 1.84 A from graphene surface. The potential barrier of Li + ion diffusion on the graphene surface, about 0.32 eV, is much lower than that of Li + ion penetrating the carbon ring which is 10.68 eV. When a vacancy of graphene exists, potential barrier about 10.25 eV for Li + ion penetrating the defect is still high, and the ability of the vacancy to sizing the Li + ion is also observed. Electronic densities of states show that the formation of a localized bond between Li atom and edge carbon of vacancy is the main reason for high potential barrier when Li + ion penetrate a vacancy. While Coulomb repulsion is the control factor for high potential barrier in case of Li + ion penetrating a carbon ring.