Acoustic metamaterials are artificial composite materials that can produce elastic wave band gaps. When the frequency of noise and vibration is within the range of elastic wave band gaps, they will be filtered by the acoustic metamaterials to achieve the effect of vibration reduction and noise reduction. Aiming at the problems of vibration and noise during ship operation, an acoustic metamaterial with a triply periodic minimal surface (TPMS) lattice structure based on local resonance theory was designed. Through simulation and COMSOL finite element software analysis, the permeability, band gap characteristics, vibration transmission loss, sound insulation effect, and the influence of different porosities and propagation medium on these characteristics are calculated. The results show that by adjusting the volume fraction of the TPMS lattice structure, a wide band gap at high frequencies can be obtained, that is, it has a certain attenuation effect on high-frequency noise. It provides new ideas for ship's water noise reduction technology and acoustic stealth technology.