We propose a double-stub resonator (DSR) based on a metal-insulator-metal (MIM) surface plasmon waveguide. The plasmon-induced absorption (PIA) effect is achieved by mutual interference between the two stub cavity modes. The transmission properties of the system are numerically simulated by the finite-difference time-domain (FDTD) method. Anomalous dispersion phenomenon can be achieved with the PIA windows based on the simulation analysis of phase response characteristics. Such anomalous dispersion effect can be used for realizing fast light effect in surface plasmonic waveguide. In addition, a multi-switch function based on the PIA effect is proposed. By simulating the influence of the changes of stub cavity′s length and the refractive index on the PIA window, the structural parameters of the switch function are optimized. Structures with these characteristics have potential applications in surface plasmon optical switches and filters and so on.