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We utilize tunable graphene plasmons to study nanometric-size molecular refractive index and vibrational modes sensing by a graphene integrated silicon grating. The great electric field enhancement and wide tunability of the localized graphene plasmons enable the proposed device accurate label-free identification of the molecular refractive index and the mid-infrared vibrational modes by detecting the resonant wavelength and the absorption spectrum before and after the protein layer formation. Our calculation results pave the way for the further development of novel cost-effective biosensors by an active plasmonic device.