Graphene holds great potential to provide efficient modulation in optoelectronic integrated circuits due to its excellent tunability in conductivity, and several types of graphene-based photonic modulators have already been demonstrated. In this Letter, a plasmonic modulator was proposed based on a groove-structured metasurface covered by a single-layer graphene sheet, in which a transverse electrical-like mode is accommodated. Our design takes advantage of the field enhancement of the plasmonic mode and overcomes the orientation mismatch between the electrical field of the free surface plasmons and the graphene plane. Therefore, this graphene-based plasmonic modulator exhibits a greatly improved modulation depth, compared with the conventional plasmonic ones. Our theoretical results also show that this modulator can work in a broadband with acceptable insertion loss, indicating possible applications in nanophotonic integrations.