The single Helmholtz resonator obtains only one absorption peak in the broad frequency range, which limits its application in reducing the noise with multiple spectra. This paper reports an acoustic multi-layer Helmholtz resonance metamaterial, which can achieve multiple absorption peaks at given low-frequency targets. Meanwhile, through adjusting structural parameters of the multi-layer Helmholtz resonator, its impedance can be altered correspondingly to realize the absorption of noise with the multi groups of specific frequencies. In this paper, in order to achieve fine absorption performance with the specific frequencies of 100 and 400 Hz for a substation noise source, the sound absorption principle of a classical Helmholtz resonator with the embedded aperture is introduced theoretically, and then two series of multi-layer Helmholtz resonance structures with different parameters are designed. Thickness of the multi-layer structure is only 1/30th of the working wavelength, and two groups of resonance peaks are generated at 100 and 400 Hz, respectively. A finite element model of the multi-layer Helmholtz resonator is constructed to simulate its absorption performance. The samples are fabricated through the 3D light-curing printing, and their sound absorption performances are detected by the standing wave method. The simulation results are in good agreement with the experimental data, and two peaks with near-perfect absorptions are achieved at the target frequencies. The multi-layer Helmholtz resonator for achievement of three groups of absorption peaks is proposed later. This work provides an effective method to design a sound absorber with multiple absorption peaks, which can promote the application of acoustic metamaterials.