Mechanism of Li diffusion at the (104) surface and in bulk of LiCoO2 is studied using density functional theory calculations. We find that there is almost no barrier for diffusion of Li between the two topmost surface layers. Results show that Li intercalation occurs by the diffusion of Li ions from the first layer to the divacancy of Li sites created by removal of two neighboring Li ions in the first and second layer. However, Li deintercalation occurs by the diffusion of Li ions from the second layer to the missing row of topmost Li sites. The energy barrier for the process of intercalation/deintercalation of Li between the second and third surface layers, which occurs by the missing-row mechanism, is also lower than that in the bulk. This finding indicates that nanosized LiCoO2 with a large surface area/volume ratio is a promising cathode material for fast charging/discharging Li-ion batteries.