We　propose　a　layer-by-layer　graphene/insulator　stacks　based　terahertz　plasmonic　sensor　of　refractive　index　of　testing　samples　using　a　prism-coupling　attenuated　total　reflection　configuration.　An　angular　interrogation　technique　has　been　used　to　explore　the　performance　of　the　sensor　in　terms　of　detecting　accuracy,　sensitivity,　and　figure　of　merit　(FOM).　From　the　analysis　of　theoretical　resonance　angle　of　the　sensor　and　the　finite　element　method　(FEM)　based　simulation,　we　reveal　that　the　number　of　graphene　layer　(N),　the　Fermi　level　energy　(E-F)　of　graphene,　and　refractive　index　of　testing　samples　have　a　great　effect　on　these　performance　parameters.　The　simulated　results　show　that　more　layers　of　graphene　will　result　in　higher　detection　accuracy　but　lower　sensitivity　and　FOM.　The　effective　detection　accuracy　can　be　improved　through　high　doping　levels　or　with　multilayer　graphene.　The　maximum　detection　accuracy　is　7.14　degree-　1　for　N　=　5　at　E-F　=　1.6eV.　The　maximum　sensitivity　is　51.0(omicron)/RIU,　along　with　a　FOM　up　to　12.75　RIU-1　for　N　=　1　at　E-F　=　1.0eV.