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The plasmonic waveguides with unsymmetrical grooves shaped metal-insulator–metal (MIM) structures are proposed in theory. For symmetrical and unsymmetrical groove structures, the transmission varies with the increasing of the groove depths and groove lengths. The filtering characteristics due to the destructive interference of the plasmonic modes are found in those subwavelength structures. The transmission line theory is utilized to interpret the transmittance and filtering phenomena. The transmission formulas are also achieved by the transmission line theory. It is found that the slow light effects are emerged in the unsymmetrical groove structures. A small group velocity (c/80) can be achieved. Finite Element Method (FEM) is conducted to verify our design.