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An asymmetric double-electrode structure composed of metal strips separated by a dielectric core layer, all on a metal slab, is proposed as a long-range surface plasmon-polariton (LR-SPP) waveguide. LR-SPP modes on asymmetric structures, including straight, S-bended, and Y-branched strips, are found by far-field measurement to be consistent with theoretical estimates. The proposed structure is inherently free from a symmetry requirement on dielectric constants between the core and cladding materials, therefore, an asymmetric double-electrode waveguide which substitutes a nonlinear medium or biofluid for the core dielectric may be essential to realization of SPP nonlinear devices or biosensors in a long-range manner.