Triply Periodic Minimal Surface (TPMS) sandwich structure has the characteristics of lightweight, high specific strength, specific stiffness, vibration, and noise reduction. There is relatively little research on its sound absorption performance. TPMS sandwich structure based on selective laser melting (SLM) technology can achieve precise control of structure type, porosity, and so on, and has broad prospects in noise control applications. In this paper, the sandwich structure is designed based on tri-periodic minimal surface implicit function, and the titanium alloy sandwich structure is formed by SLM technology, and the sound absorption performance of titanium alloy TPMS sandwich structure is studied. The effects of volume fraction, panel thickness, and cell layer number on the sound absorption performance of the two TPMS structures were systematically analyzed using the transfer function method. The results show that: The GP10 sandwich structure with the volume fraction of 20%, the thickness of the panel is 1.0 mm, and the number of cell layers is 3C parameter combination has better sound absorption performance and higher sound absorption bandwidth, and the sound absorption coefficient is 0.36. For Ti6Al4V sandwich sound absorption structure, it is not suitable to design too thick panels. When the volume fraction is lesser, the increase of the tortuosity factor τ improves the sound absorption performance of the two structures, and excessive volume fraction leads to a decrease of sound absorption performance. The increase of cell layers can broaden the sound absorption bandwidth of the two structures, and the sound absorption capacity increases and then decreases in the range of 150–6400 Hz. The Gyroid structure mostly exhibits resonance sound absorption mechanism, while the Diamond structure exhibits resonance sound absorption mechanism combined with the viscous loss of sound wave. The work done in this paper can provide a theoretical basis for the study of the sound absorption characteristics of TPMS sandwich structure.