Graphene is superior as a contact with silicon active materials and their composite show very small volume expansion during charge processes. However, further study on atomistic-scale mechanism of the interaction between Li and Graphene-Silicon (Gra/Si) system is very challenging for current experimental technologies. In this work, the mechanism of Li adsorption on a Gra/Si system is investigated using density functional theory. Based on the calculated results of binding energies, charge transfer, charge density difference, mean squared displacement and diffusion constant, it concluded that the incorporation of graphene can significantly enhance the electrochemical performance of silicon as high performance anode material, which consists with the experimental results. A theoretical capacity of 2896 mAhg(-1) is obtained, it is closed to the first cycle capacity of 2634 mAhg(-1) in experiment. Moreover, the origin of irreversible capacity of Gra/Si system is investigated. The shorter bond lengths Li-S and Li-C are related to strong Li-C and Li-Si connections and irreversible capacity loss during lithiation. Then a reversible capacity of 2383 mAhg(-1) is obtained by excluding the Li atoms with shorter bond lengths, and is comparable to the reversible capacity of 2497 mAhg(-1) in experiment. The proposed computational frame can be used to evaluate and design nanocomposite anode materials for lithium-ion batteries.