A novel broadband graphene modulator based on a plus-shaped plasmonic slot waveguide (PSPSW) has been demonstrated. The designed modulator includes four square silver nanowires and a graphene-${{\rm Al}_2}{{\rm O}_3}$Al2O3-graphene layer. Four silver nanowires are separated from each other by an ${{\rm SiO}_2}$SiO2 gap layer, forming a plus-shaped slot waveguide. This modulator overcomes the challenge of polarization mismatch between the electric field of the plasmonic mode and the graphene plane. The highly confined plasmonic mode can strongly interact with the graphene sheets. The properties of three eigenmodes and the effect of the geometric parameters have been studied. By geometric optimization, this modulator could offer a high modulation depth of 1.13 dB/µm, a wide operation wavelength ranging from 1200 to 1600 nm, and a large modulation bandwidth of 95 GHz. This design may promote the development of graphene-based nanophotonic devices.