Silicon/carbon composite is one of the most potential high-capacity anode materials for lithium-ion batteries. The interface state between silicon and carbon of silicon/carbon composite is an important factor affecting its electrochemical performance. In this paper, Si _n( n≤ 6) clusters with different numbers of Si atoms are constructed on graphene as a structural unit of carbon material. The geometric configuration, structure stability and electronic property of Si _nclusters adsorbed on graphene (Si _n/Gr) are studied by the first-principles method based on density functional theory (DFT). The results show that when the number of Si atoms n≤ 4, the Si _nclusters are preferentially adsorbed on graphene in a two-dimensional configuration parallel to graphene. When n≥ 5, the Si _nclusters are preferentially adsorbed on graphene in a three-dimensional configuration. With the increase of the number of Si atoms n, the thermodynamic stability of Si _nclusters on graphene decreases significantly, the interface binding strength between Si _nclusters and graphene decreases, and the charge transfer between Si _nclusters and graphene becomes less. At the same time, the storage capacity of Li atoms in Si _n/Gr complex is also studied. Li atoms are mainly stored on the graphene surface near Si _nclusters and around Si _nclusters. The complex synergistic effect of Si _nclusters and graphene enhances the thermodynamic stability of Li adsorption. When n≤ 4, storing two Li atoms is beneficial to improving the thermodynamic stability of xLi-Si _n/Gr system, and the thermodynamic stability decreases with the increase of Li atom number. When n≥ 5, the thermodynamic stability of xLi-Si _n/Gr system decreases with the increase of Li atom number. In the xLi-Si ₅/Gr system, the C-C bond and Si-Si bond are mainly covalent bonds, while the Li-C bond and Li-Si bond are mainly ionic bonds with certain covalent properties.