We investigate the electrically controlled light propagation in the metal–dielectric–metal plasmonic waveguide with a sandwiched graphene monolayer. The theoretical and simulation results show that the propagation loss exhibits an obvious peak when the permittivity of graphene approaches an epsilon-near-zero point when adjusting the gate voltage on graphene. The analog of electromagnetically induced transparency (EIT) can be generated by introducing side-coupled stubs into the waveguide. Based on the EIT-like effect, the hybrid plasmonic waveguide with a length of only 1.5 μm can work as a modulator with an extinction ratio of ～15.8 dB, which is 2.3 times larger than the case without the stubs. The active modulation of surface plasmon polariton propagation can be further improved by tuning the carrier mobility of graphene. The graphene-supported plasmonic waveguide system could find applications for the nanoscale manipulation of light and chip-integrated modulation.