FGPMs (functionally gradient porous materials) can satisfy multifold functional constraints with minimizing weights as they are advanced composite materials showing hierarchical mechanical properties. However, tailoring the graded relative elasticity distribution of the FGPMs according to demands is still a big trouble, especially for the FGPMs with complex interior structures. In this context, this paper proposes an improved FGPMs design method for tailoring the graded relative elasticity field with stochastic Voronoi structures, which are driven by the FEA (finite element analysis) results. Firstly, a kind of open-cell porous structure is built for FGPMs based on 3D Voronoi diagrams and implicit surfaces. An external frame is generated outside the Voronoi structure to enhance the modeling adaptability and keep geometric and mechanical continuity. Then, two mapping models are established for tailoring the elasticity fields of the FGPMs. One is from the relative elasticity field to the relative density field based on Ashby-Gibson model, wherein, the relative elasticity field is obtained from the FEA results. The other one is from the obtained relative density field to the Voronoi site density field that drives the generation of the open-cell Voronoi porous structure. Finally, the proposed method is experimentally and numerically validated. The results show that both the geometric modeling ability and the elasticity tailoring accuracy are superior, and the FGPMs produced by our method have better mechanical performance compared to other FGPMs.