Elastic metamaterials have attracted much attention owing to their capability in controlling elastic vibration propagation. In this work, we numerically study the elastic properties of polymer Nylon-12 based triply periodic minimal surfaces (TPMS). Two typical lattice structures, Primitive and Schoen’s F-RD surfaces, are discussed with an emphasis on the relationship between their filling fraction and elastic band structures. Our simulation results show that both TPMS structures exhibit bandgaps in the low-frequency range between 1.2 kHz and 1.7 kHz. The bandwidth of the bandgap is monotonically increased with increasing the filling fraction. As compared to a single bandgap in the FRD-TPMS structures, the number of bandgaps for Primitive-TPMS is reduced as the filling fraction is increased from three to one. Our eigenmode study indicates the disappearance of the bandgap results from the shape changed from an open cavity to a structure with an internally closed cavity This study indicates that by tuning the relative density, suitable bandgaps can be designed for acoustic applications in the specific frequency range.