Studies have shown that under in-plane impact loading, negative Poisson's ratio of honeycomb sandwich structure has a good energy absorption compared with the conventional cellular sandwich structure. So, it can be used to protect the key components and the crew from being hurt in the crash accidents. In the design of collision avoidance, both of the energy absorption and the deformation should be considered. In this paper, we designed a honeycomb structure with density gradient which had a good behavior in crashworthiness. Based on the honeycomb sandwich structure with negative Poisson's ratio, we changed the density gradient of the core and studied the energy absorption and the deformation of the structure under impact loading. First, we divided the core into three layers which had different densities. And each layer had the same thickness and the same kind of material. Then, we gave the different permutation and combination of the three layers. In addition, we established the finite element models of the combinations. Based on the models, the in-plane impact was loaded to do the simulation calculation. The total energy absorption of each sandwich structure was figure out. Besides, the deformation of the inner plate was also calculated. Integrated the two indicators, the most optimal density distribution could be got. This study also has a profound significance in the lightweight structure design. With the development of the processing technology, the functionally gradient honeycomb structure with negative Poisson's ratio will be widely used in the areas of aviation, navigation, transportation and so on.