Abstract: The pore structure of natural reservoirs is complex,where the coexistence of pores and throats and their scale-invariance distribution have been widely observed. Although the fractal dimension D is easy to obtain by the clas- sical number-size model Rns or its variants,it is hard to guarantee that the many-to-one relationship between Rns and D is unique for reverse modeling. Meanwhile,the unclear nature in complexity types and their assembly patterns of fractal objects causes the effective characterization of the complex pore structure in natural reservoir very difficult. Therefore, it is of fundamental importance for a clear understanding of the complexity types to quantitatively represent their as- sembly pattern in fractal pore-throat porous media,because all these would affect the occurrence and migration of oil and gas significantly. The newly emerged fractal topography points out that a fractal set is a dual-complexity system,in which the original complexity and behavioral complexity are coexisting but independent to each other. In other words, the former determines the scaling type of single or multi scale,phase,and type,while the latter decides the scale-invar- iant properties of self-similarity,self-affinity,and multifractality. In this study,the authors identify the complexity types in fractal pore-throat porous media,and clarify the original complexity composed of pore,throat and its connectivity. In addition,the authors propose an approach to effectively represent the original complexity of pore-throat coupling geom- etries by Voronoi model,define the scale-invariance behavioral complexity as per the fractal topography theory,and de- velop an algorithm for the quantitative representation of fractal pore-that porous media. Thereafter,the authors model the fractal pore-throat porous media with diverse complexity assembly,investigate the effects of original and behavioral complexities of the total complexity of pore structure,analytically derive the estimation models of porosity and specific surface area,and verify the validity of the novel algorithm.