A broadband modulator with hybrid plasmonic graphene waveguide is proposed. The waveguide is very convenient to transfer graphene and improve fabrication tolerance. We use tip enhancement effect of graphene-based hybrid wedge SPPs mode to enhance light absorption modulation. The interaction between the hybrid plasmonic graphene structure and the optical field is numerically investigated. We get the geometrical optimization value by sweeping the parameter with FDTD method. The result demonstrates that modulation depth of our proposed modulator exceeds 3 dB when wavelength changes from 3.3 to 3.7 µm. Moreover, compared with previous papers, our proposed modulator can obtain broader modulation bandwidth (156.49 GHz) and need lower power consumption (477 fJ/bit), which has a better performance in potential applications such as optoelectronic countermeasure systems and optical signal processing. © 2021 Elsevier GmbH