Topologically protected plasmonic states with wide topological band gaps provide unprecedented robustness against disorder-induced backscattering. In this study, we design a graphene bi-layer metasurface that possesses valley-Hall topological plasmonic modes in a nontrivial bandgap. In particular, the breaking of mirror symmetry of two graphene layers is achieved via a horizontal shift of the hole lattice of the top layer, which leads to topologically protected edge modes in the nontrivial bandgap. The corresponding band dispersion of the topological edge modes shows unidirectional propagation features. Moreover, we have designed a sensitive molecular sensor based on such graphene bi-layer metasurfaces, using the fact that the chemical potential of graphene varies upon adsorption of gas molecules. This effect leads to a marked variation of the transmission of the topological mode, and thus a sensing device with large sensitivity can be realized.