The precise arrangement of single entity is a crucial objective of nanoscience and holds great promise in various fields such as biology and material science. In this work, we develop a "DNA framework-mediated geometric renormalization" (DFMGR) strategy to reassemble gold nanoparticles into specific geometric shapes on a 2-dimensional (2D) fluidic membrane interface. Cholesterol-modified AuNPs are randomly anchored on the supported lipid bilayer (SLB) via the cholesterol-lipid interaction. We demonstrate that AuNPs are laterally mobile on SLB and could be further rearranged into a specific geometric shape by DNA framework containing algebraically topological DNA arms. Using scanning electron microscope (SEM) imaging approach, simple geometric shapes, such as points assembled by monomers, line segments assembled by dimers, triangles assembled by trimers are visually presented. Interestingly, we found that the statistic angle (58.77°) and side length (12.21 nm) of triangles obtained from SEM images were both agreed well with the theoretical angle of 60° and side length of 12.58 nm. And the relative error of the angle calculated was as low as 0.33 %. These results indicated that the DFMGR strategy showed precise regulation ability for the AuNPs renormalization. We believe that DNA framework-mediated geometric renormalization strategy would be a powerful means for regulating ligand-receptor interactions in biosystems and for nanoparticle assembling in material science.