Light propagation through a metal/nonlinear dielectric material/metal (M-NL-M) structure is numerically studied. The design parameters of the M-NL-M structure are found with the waveguide theory so that the structure only supports the symmetric surface plasmon polaritons (SPP(0)) mode and the antisymmetric surface plasmon polaritons (SPP(1)) mode. The coupling between the two modes within the M-NL-M structure is exploited. Through controlling the propagation constants of the two modes with the intensity-dependent dielectric constant of the nonlinear Kerr material, an effective all-optical control of plasmonic signal modulator can be realized with this M-NL-M structure.