A polarization-insensitive graphene-assisted electro-optic modulator is proposed. The orthogonal T-shaped metal slot hybrid plasmonic waveguide allows the polarization-independent propagation of transverse electric field mode and complex mode. By the introduction of dual-layer graphene on the ridge waveguide, the polarization-insensitive modulation depths of the TE mode and complex mode are 0.511 dB/µm and 0.502 dB/µm, respectively. The 3 dB bandwidth of the modulator we have proposed is about 127 GHz at the waveguide length of 20 μm. The power consumption of 72 fJ/bit promised potential graphene electro-optic modulator applications for on-chip interconnected information transfer and processing.