A sandwich structure with minimal surfaces has advantages of high specific rigidity and good energy absorption and has shown a wide range of application prospects in practical engineering. But its sound insulation performance has not been thoroughly studied. The sound insulation performance of the D-type and I-WP type sandwich structure with the triply periodic minimal surface is studied using numerical and experimental methods in this paper. First， based on the theory of acoustic-vibration coupling， a finite element （FE） model of sandwich structure with the triply periodic minimal surface cores is established. Then， the accuracy of the FE model is verified by the acoustic impedance tube method. Finally， as the thickness of the sandwich core t， the thickness of the panel d， the elastic modulus E， the minimal surface constant C and the periodic constant T are the key parameters their influences， on the acoustic insulation performance of the sandwich structure with the minimal surface is systematically analyzed by using the validated finite element model. Results reveal that the I-WP type sandwich structure has sound insulation of up to 60dB in the 4400Hz-5000Hz frequency band. This research is expected to provide new solutions for passive sound insulation of lightweight structures in high-speed trains and other fields.