For the purpose of low-frequency vibration isolation and noise reduction, combined with the nested mode of spider web, a new concave star bionic acoustic metamaterial was proposed in this paper. Based on the finite element method (FEM) and Bloch theory, the effects of vertex connection mode, nesting level (n), and rotation angle (α) on the band gap distribution, transmission spectrum, and isofrequency line of concave star structure were discussed. The results showed that the two-dimensional (2D) concave star structure had the lowest opening frequency of the first band gap when the vertices coincide and n = 3; when α = 45°, the three-dimensional (3D) concave star structure had the widest band gap distribution and the lowest first band gap in the frequency range within 1000 Hz. The correctness of the simulation results was verified by experiments. These findings can provide a new idea for low-frequency vibration isolation and noise reduction.