For low-frequency noise control problems, a Helmholtz-type phononic crystal with an adjustable chamber was constructed. The inner chamber of the structure is divided into upper and lower chambers by a diaphragm connected by a movable telescopic screw. Meanwhile, an arch-shaped opening channel is adopted. Characteristics of bandgap and sound insulation of the structure are analyzed by finite element method, and equivalent models of the structure at the starting frequency and cut-off frequency of the bandgap are constructed by “acoustic-force analogy” method. The results show that the designed structure can generate six complete bandgaps within 500 Hz, and the lowest bandgap frequency can reach 31.34 Hz. At the same time, it shows good sound insulation performance in each bandgap frequency band, and the maximum sound insulation is up to 111.95 dB. Finally, by adjusting the telescopic screw and changing the cavity structure layout, multiple resonant bandgaps can be connected to form a wide bandgap, and achieve the purpose of adjusting the sound insulation band. This design provides a new idea for the sound insulation performance of Helmholtz type phononic crystals.