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We investigate the polarization singularities in the metal-insulator-metal (MIM) plasmonic waveguide structure. It turns out that there exist L-line and C-point polarization singularities for the antisymmetric plasmonic mode in the MIM plasmonic waveguide. These polarization singularities have unique properties because they exist on a subwavelength plane parallel to the direction of propagation of light along the core. We believe that our findings can expand the understanding of polarization distributions in nanoscale plasmonic structures.