Understanding Li ion intercalation at the electrode-electrolyte interface is critical for predicting and optimizing the performance of lithium-ion secondary batteries (LIB). In this work, we investigate the impact of the electrode surface chemical composition, in particular the edge termination of graphite anodes, on the energetics and rate of intercalation/de-intercalation and the related Li ion solvation structure near the interface. We carried out extensive first-principles molecular dynamics simulations of a prototypical electrolyte consisting of ethylene carbonate (EC) organic solvent containing dissolved LiPF₆ salt, in contact with armchair- and zigzag-oriented graphite surfaces. By considering a variety of surface terminations, including H, 1:1 H/OH, and carbonyl, we find that surface composition shows significant effects on the energetics of Li⁺ intercalation. Specifically, the carbonyl-terminated surfaces exhibit a significantly larger energy barrier for Li⁺ insertion due to a complex interplay between the surface polarization, electronic charge transfer and the formation of pseudo-solvation shells involving surface chemical species, in sharp contrast to the H and 1:1 H/OH terminations. This work extends generally to a variety of solid/liquid interfaces in LIB, where surface chemical interactions play an important role in kinetics.