Based on the design concept of functionally graded materials, the composite gradient double-arrow auxetic structures were designed and fabricated. The thickness of core layers demonstrates an increasing trend for positive gradient structure, while a decreasing trend for negative gradient structure. The thickness of core layers keeps constant for homogeneous structure. The dynamic response and failure modes of the double-arrow auxetic structure with different gradient distributions of wall thickness were obtained by foam projectile impact experiments. The influence of the gradient distribution of core wall thickness on the impact resistance of composite double-arrow auxetic structures under local impact load was investigated. The results demonstrated that the gradient distribution of core wall thickness has an important influence on the dynamic response and failure modes of the structure. The negative gradient auxetic structure revealed more excellent impact resistance compared with the positive gradient auxetic structure. In addition, the response of the gradient double-arrow auxetic structure under local impact load was simulated by ABAQUS/Explicit, and the simulation results were in good agreement with the experimental results. Combined with the experimental and numerical simulation results, it was found that the negative gradient distribution of core wall thickness had an obvious improvement on the impact resistance of composite double-arrow auxetic structure under local impact load.