In recent years, the vibration and noise reduction performance of military aircraft has become an important index to measure its performance. In order to solve the problem of low-frequency noise generated by military aircraft, a novel Helmholtz two-dimensional phononic crystal is constructed in this paper. The structure adopts maze-shaped air channel and adds rigid oscillators. On condition that the lattice constant is 62 mm, the lower limit of the first band gap is reduced to about 15 Hz. The structure has four complete band gaps in a range of 0–500 Hz, specifically, they being 15.223–17.464 Hz, 107.46–200.68 Hz, 231.18–310.68 Hz, and 341.14–404.49 Hz. In addition, the sound reduction index of the structure reaches 25 dB at 15 Hz, and two peaks higher than 150 dB appear at about 107 Hz and 231 Hz. which shows distinct sound insulation capability in the low-frequency range. It has engineering significance in controlling the low-frequency noise in the aircraft cabin. The cause of the band gap is explored by analyzing the vibration mode and sound pressure field. The “spring-oscillator” of the structure model is established by the method of “Mechanical-acoustic analogy”. The finite element method and transfer matrix method are used to calculate the upper limit and the lower limit of the first band gap. It is shown that for the first gap of the structure, the results obtained by the two methods are similar, which indicates the correctness of the model hypothesis. Secondly, the effects of structural parameters such as the lattice constant, the length of the air channel and the oscillator material on the first band gap are investigated by finite element method and equivalent model method. It is obtained that the increase of the length of air channel and lattice constant will reduce the lower limit of the first band gap, with other structural parameters remaining unchanged. Moreover, the increase of the density of the oscillator material can effectively reduce the upper limit and lower limit of the second band gap, which further reveals the essence of the formation of the band gap of the structure and verifies the accuracy of the equivalent model. This study provides theoretical support for low frequency noise control and broadens the design of low-frequency phononic crystals.