Hybrid plasmonic waveguide (HPW) has received extensive attention recently due to its excellent performance of tight field confinement and low propagation loss. In this work, the transmission spectra of hybrid plasmonic waveguide Bragg gratings (HPWBGs) composed of two alternately arranged low refractive index dielectric materials are studied, combining the finite element method (FEM) and transfer matrix method (TMM). Meanwhile, by changing the width of the outermost layer of the waveguide, the influence on transmission spectra under different optical admittance matching conditions are discussed through admittance matching theory. Theoretical calculations and simulation results show that a specific thickness of the matching layer has a specific influence on the pass band or the forbidden band of a specific frequency range on the transmission spectrum. The transmission characteristics of the low-frequency or high-frequency pass band and the band gap can be optimized by adjusting the thickness of matching layer to obtain the admittance match or mismatch conditions. This result provides a good theoretical basis and design method for preparing photonic devices for requirements in different wavebands.