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_n clusters 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_n clusters are preferentially adsorbed on graphene in a two-dimensional configuration parallel to graphene. When n ≥ 5, the Si_n clusters 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_n clusters on graphene decreases significantly, the interface binding strength between Si_n clusters and graphene decreases, and the charge transfer between Si_n clusters 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_n clusters and around Si_n clusters. The complex synergistic effect of Si_n clusters 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-Si₅/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.