The gradient design of a fine grain structure on the surface and coarse grain structure in the substrate gives nano metallic materials both high strength and plasticity. Inspired by the concept of gradient design of grain sizes in materials science, this paper shows the design of the gradient Voronoi polygonal honeycomb structure. The quasi-static uniaxial tensile deformation processes of both, gradient and uniform, Voronoi structures were studied and it was found that the gradient design of the honeycomb cell size greatly improves the tensile property and strain energy storage of the Voronoi structure.