The star-shaped negative Poisson’s ratio structure is used as the core of sandwich panels. The dynamic model of a sandwich plate is established，and the equivalent elastic parameters of sandwich layer are derived. The equations of motion of sandwich plates are derived based on Hertz theory，first order shear deformation theory and Hamilton principle. Then，the equations of motion are solved by navier method. The contact force of the impact model is obtained through the spring-mass model with two degrees of freedom，and the lateral displacement of the sandwich plate after impact is calculated by Duhamel integral. The predicted results of plate contact force and lateral displacement are compared with the published papers to verify the accuracy. Meanwhile，the low-velocity impact response of star-shaped negative Poisson’s ratio sandwich panels is also compared with the negative Poisson’s ratio concave hexagonal honeycomb sandwich panels，and the influence of the parameters of sandwich panels is also discussed. When the impact velocity increases，the maximum contact force and the maximum lateral displacement of the sandwich plate also increase，while the duration of the impact response decreases. The greater the thickness ratio of the sandwich plate is，the better the impact performance of the sandwich plate will be. The smaller the side length ratio of cell is，the better the impact performance of sandwich plate will be. The increase of the cell concave angle enhances the impact performance of the sandwich panel. This study can provide some reference for the study of impact resistance of negative Poisson’s ratio metamaterial structures and sandwich panels.