In order to achieve a balance between sound insulation and ventilation, a novel acoustic metamaterial of air-permeable multiple-parallel-connection folding chambers was proposed in this study that was based on Fano-like interference, and its sound-insulation performance was investigated through acoustic finite element simulation. Each layer of the multiple-parallel-connection folding chambers consisted of a square front panel with many apertures and a corresponding chamber with many cavities, which were able to extend both in the thickness direction and in the plane direction. Parametric analysis was conducted for the number of layersnland turnsnt, the thickness of each layerL2, the inner side lengths of the helical chambera1, and the intervalsamong the various cavities. With the parameters ofnl= 10,nt= 1,L2= 10 mm,a1= 28 mm, ands= 1 mm, there were 21 sound-transmission-loss peaks in the frequency range 200–1600 Hz, and the sound-transmission loss reached 26.05 dB, 26.85 dB, 27.03 dB, and 33.6 dB at the low frequencies 468 Hz, 525 Hz, 560 Hz, and 580 Hz, respectively. Meanwhile, the corresponding open area for air passage reached 55.18%, which yielded a capacity for both efficient ventilation and high selective-sound-insulation performance.