The control of noise pollution in the low-frequency domain with various spectrum ranges requires the development of a novel tunable sound absorbing material, and a multilayer stackable grouped acoustic metamaterial (MSG-AM) is proposed in this research to obtain the optimal noise reduction effect while minimizing the occupied space. The MSG-AM includes four layers with the eight Helmholtz resonators in each layer divided into three groups, and the total 32 resonators in different layers are connected in parallel. The sound absorption property of each layer is optimized by the joint simulation of finite element simulation and particle swarm optimization algorithm, and the average sound absorption coefficient (SAC) reaches 0.8609 for the first layer in the 535–650 Hz, 0.7126 for the second layer in the 782–937 Hz, 0.9285 for the third layer in the 650–782 Hz, and 0.7615 for the fourth layer in the 435–535 Hz, respectively. The four layers can be combined flexibly to gain the desired sound absorption property in the expected frequency range, and the sequence of multiple layers is a critical factor. The average SAC of the MSG-AM with four layers is improved from 0.3696 for 4 + 1 + 3 + 2 to 0.8726 for 2 + 3 + 1 + 4, and it is better to put behind the layer to obtain absorption in the low-frequency domain and put in front the layer to achieve absorption in the high-frequency domain. The sound absorption mechanism is revealed intuitively through the distributions of thermal power densities, which certify that there exists Helmholtz resonance and Fabry–Pérot resonance effects simultaneously. The proposed MSG-AM is conducive to guarantee the effective control of variable noise.