To solve the problem of low-frequency noise in aircraft cabin, a Helmholtz periodic structure with double labyrinth tubes was proposed in this paper. The design of labyrinth tubes greatly increases the length of tubes of Helmholtz resonator, reducing the lower limit of low-frequency band gap. The design of double opening tubes can increase the region of local resonance of the phononic crystal, therefore, the number of low-frequency band gaps increases. Firstly, the band structure and sound insulation characteristics of the structure in the frequency range from 0 Hz to 500 Hz were characterized by finite element method (FEM). It is found that the structure has multiple complete low-frequency band gaps in the frequency range from 0 Hz to 500 Hz, showing an excellent low-frequency sound insulation characteristic. Secondly, to reveal the mechanism of band gap, the equivalent circuit model was established by the method of electro-acoustic analogy. Finally, the influence factors of band gaps were analyzed by FEM and equivalent model. It is found that increasing the length of the tubes can effectively reduce the lower limit of the band gap, and a smaller lattice constant is beneficial to widen the band gap. The research in this paper further explores the influence of phononic crystal structure design on band gap and provides a new method for low-frequency noise reduction of aircraft cabin.