Flexible control of terahertz waves is now a research hotspot. Based on the electromagnetic theory the dispersion relation and field distributions in a plasmon-assisted parallel-plated waveguide are deduced. The transmission property of such a waveguide is obtained and confirmed by the full-wave simulation. Results show that the plasmon-assisted parallel-plated waveguide shows a band gap characteristic, and the cutoff frequency of the upper sideband is equal to the plasmon frequency; generally, the thinner the plasmon layer, the higher the cutoff frequency will be, and the narrower the bandwidth will become. Emergence of the band gap is due to the excited surface plasmon polaritons, and the coupling between surface plasmon and the medium in the waveguide. Besides, the influence of plasmon frequency and collision frequency on the transmission properties is investigated, and a method for adjusting the filter characteristic of the waveguide by tuning the plasmon frequency is proposed. Moreover, the plasmon layer is realized by a textured metallic structure, and a sensing model based on the parallel-plated waveguide is designed. Simulation results show that a 0.1 percent change in permittivity of the sample materials filling in the groove will give rise to a significant change of the cutoff frequency, which is 1.8 GHz in average; interestingly, different liquid samples such as nitrogen, gasoline, paraffin, glycerine and water can be identified through detecting the change of cutoff frequency, which further confirms the excellent terahertz sensing characteristic of the proposed sensor. This work may be helpful for the study of terahertz wave transmission, and may have potential applications in the design of terahertz devices.