The influence of the Poisson's ratio of the foam on the energy absorption of the foam-filled tube is investigated in this paper. Firstly, the relationship between the mechanical properties and the structural parameters of the 3D lattice structure is calculated by using the theory of material mechanics. The finite element analysis software ABAQUS is used to simulate the axial dynamic response of cylindrical tubes filled with conventional and negative Poisson's ratio foams. Based on this, the interaction between the tube wall and foam is analyzed in detail. Combining the structural properties of both the positive and negative Poisson's ratio foams, a new foam model with mixed Poisson's ratio (MPR) is proposed, and the crashworthiness of three different types of tubes, namely the sandwich double tubes filled with positive, negative and mixed Poisson's ratio foams, is analyzed. The results show that the interaction between the foam and the tube wall has a significant effect on the energy absorption performance. The sandwich double tube filled with MPR foam has better specific energy absorption (SEA) and stronger interaction than those filled with pure positive or negative Poisson's ratio foam. This study provides a new insight into crashworthiness design of foam-filled structures.