In this paper, a novel method based on the space-filling design and 2D-Voronoi method was studied to design the in-plane gradient continuous controllable sandwich structures. In this method, the radial gradient distribution of the relative density in the sandwich structure plane was realized by controlling the distribution function of the sites, and the impact resistance of the sandwich structure was designed. Gradient sandwich panels with different face sheet thicknesses were fabricated by 6061O Aluminum alloy for drop-weight impact experiments, and a 3D-finite element analysis model was established by Abaqus/Explicit, and the numerical simulation results were in good agreement with the experimental results. Based on the deformation mechanism of the gradient sandwich panels under low-velocity localized impact loading obtained by experiments and simulations, a theoretical analysis model of the dynamic response of the gradient sandwich panel under low-velocity localized impact loading was established based on the ideal rigid plastic metal material, and the deformation mode and energy absorption mechanism of the panel and core layer were analyzed. The parameters of the distribution function of the sites were analyzed, the influence of the distribution function on the impact resistance of the gradient sandwich panel was obtained, and the regulation mechanism of the distribution function parameters on the mechanical properties was clarified. To establish the multi-objective optimization problem, the site distribution function parameters were selected as the design variables, and the impact resistance of the gradient sandwich panel under low-velocity localized impact loading as the optimization goal. Utilized the design of experiment method, surrogate model technology, and multi-objective genetic algorithm, the Pareto set was obtained, and the optimal design was obtained by the minimum distance selection method. It was verified that the design method of gradient continuous controllable sandwich structure studied in this paper is feasible and effective.