The tension-shear chain model and 2D finite element model of nacre—a kind of stacking composite material—are built up, and its band gap is computed based on a multi-level substructure scheme. The results show that the nacre-like material is a kind of Bragg phononic crystal holding a relatively wide first band gap in low frequency domain and several flat bands in high frequency domain. So this kind of material can lead to the vibration reduction in a wide frequency range. Moreover, these materials are more efficient to realize the goal of vibration reduction in low frequencies, because it doesn’t have the Fano-like interference phenomena, which will happen in the locally resonant phononic crystals for the mechanism of their band gaps. Furthermore, the transmission characteristics are computed to verify the result of band gap. The further research demonstrates that band gap characteristics are mainly influenced by density of the mineral (“Brick”) component and elastic modulus of the protein (“Mortar”) component and the first band gap of nacre-like material subjects to the coupling influence of the two material parameters. An appropriate match of the two material parameters can contribute to a larger relative band gap. And the band gap is adjustable as well, which makes the nacre-like material a novel idea for the design of new vibration reduction structure.