A small quantity of monolayer graphene flakes is doped in a nematic liquid crystal (LC), and the effective polar anchoring strength coefficient between the LC and the alignment substrate is found to increase by an order of magnitude. The hexagonal pattern of graphene can interact with the LC's benzene rings via π-π electron stacking, enabling the LC to anchor to the graphene surface homogeneously (i.e., planar anchoring). When the LC cell is filled with the graphene-doped LC, some graphene flakes are preferentially attached to the alignment layer and modify the substrate's anchoring property. These spontaneously deposited graphene flakes promote planar anchoring at the substrate and the polar anchoring energy at alignment layer is enhanced significantly. The enhanced anchoring energy is found to impact favorably on the electro-optic response of the LC. Additional studies reveal that the nematic electro-optic switching is significantly faster in the LC-graphene hybrid than that of the pure LC.