A terahertz plasmonic waveguide sensor is experimentally demonstrated to utilize surface waves propagated in a onedimension metal grating that constructed on a plastic ribbon waveguide. The grating conformation couples evanescent waves of a subwavelength terahertz waveguide onto the metal surface and highly confines the extended powers within λ/22-range for the phase-matching condition. The confined terahertz waveguiding waves resemble surface plasmonpolaritons but transmit with almost zero dispersion when the coupled surface waves interfere along the metal grating. Based on the dispersion-free guidance, there is Bragg reflection dominated by grating periods and strongly dependent on the refractive index of surface plasmon-polaritions. We successfully detect different thicknesses of polyethylene layers covered on the metal grating with thickness resolution of 1μm when the effective waveguide indices are modified in the vicinity of the metal grating, corresponding to 0.01-index variation. Potentially, terahertz subwavelength ribbon waveguide based plasmonic sensors could be manipulated to detect molecules with extremely low-density or small thickness in the metal-dielectric interface for probing pollution particles and any label-free detection.