A face-to-face system of double-layer three-dimensional arrays of H-shaped plasmonic crystals is proposed, and its transmission and filtering properties are investigated in the terahertz regime. Simulation results show that our design has excellent filtering properties. It has an ultra-wide bandgap and passband with steep band-edges, and the transmittance of the passband and the forbidden band are very close to 1 and 0, respectively. As the distance between the two face-to-face plates increases, the resonance frequency exhibits a gradual blueshift from 0.88 THz to 1.30 THz. Therefore, we can dynamically control the bandwidths of bandgap and passband by adding a piezoelectric ceramic plate between the two crystal plates. Furthermore, the dispersion relations of modes and electric field distributions are presented to analyze the generation mechanisms of bandgaps and to explain the location of bandgaps and the frequency shift phenomenon. Due to the fact that our design can provide many resonant modes, the bandwidth of the bandgaps can be greatly broadened. This paper can serve as a valuable reference for the design of terahertz functional devices and three-dimensional terahertz metamaterials. A face-to-face system of double-layer three-dimensional arrays of H-shaped plasmonic crystals is proposed, and its transmission and filtering properties are investigated in the terahertz regime. Simulation results show that our design has excellent filtering properties. It has an ultra-wide band gap and passband with steep band-edges, and the transmittance of the passband and the forbidden band are very close to 1 and 0, respectively. As the distance between the two face-to-face plates increases, the resonance frequency exhibits a gradual blueshift from 0.88 THz to 1.30 THz. Therefore, we can dynamically control the bandwidths of bandgap and passband by adding a piezoelectric ceramic plate between the two crystal plates. the generation mechanisms of bandgaps and to explain the location of bandgaps and the frequency shift phenomenon. Due to the fact that our design may provide many re sonant modes, the bandwidth of the bandgaps can be greatly broadened. This paper can serve as a valuable reference for the design of terahertz functional devices and three-dimensional terahertz metamaterials.