Negative Poisson's ratio (NPR) material perform well in shear resistance, impact resistance, and fracture resistance. In this study, a novel honeycomb sandwich panel is introduced, named Concave Triangular Honeycomb Sandwich Panel (CTHSP), which employs a concave triangle structure with NPR effect as the core layer. The study on the static and dynamic performance of CTHSPs are conducted through numerical simulation. Specifically, the influence of main geometric parameters (single cell size a, core layer thickness t, face-plate core layer thickness ratio h/H, concave angle α) on the bending stiffness, buckling critical load and natural frequency of CTHSPs are studied. Moreover, a new index of specific stiffness is introduced to evaluate the advantages of lightweight and high strength of the sandwich panels. The above research can provide a basis for the selection of CTHSPs in practical application.