This paper focuses on the Li-storage performances and the stabilities of the hybrid structure of different lattice planes of the silicon clusters and graphene by the first-principles theory. In this paper, we calculate the binding energy, the adsorption energy, and the PDOS of the hybrid structure of the different heights and sizes of the silicon clusters and graphene. We figure out that strong Si-C bonds between the silicon cluster and graphene can form. Especially, the hybrid structure of the silicon clusters with plane (111) and graphene performs best with the highest formation energy and the outstanding stability. According to the calculation of Li-absorption energy, we conclude that the location of the silicon cluster near the graphene has higher possibility and higher absorption energy of the Li storage, owing to the charge transfers between lithium and carbon, and between lithium and silicon. Because the graphene is used, the deformation of the interface of the silicon cluster can be obviously reduced during the absorption of Li, which brings about a good future for the hybrid structure used as the battery anode materials.