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The through-plane permeability is of great importance for understanding the transport phenomenon in anisotropic fibrous porous material. In this paper, a novel pore-scale model based on the equilateral triangle representative unit cell (RUC) and capillary bundle model is developed for the fluid flow through the anisotropic fibrous porous material according to fractal theory, and the effective through-plane permeability is presented accordingly. The digital structures of the fibrous porous material are generated by a fractal stochastic method (FSM), and the single-phase fluid flow through the 3D-reconstructed model is simulated by using the finite element method (FEM). It was found that the effective through-plane permeability depends on the fiber column size, porosity, and fractal dimensions for pore and tortuosity. The results show that the predicted through-plane permeability by the present fractal model indicates good agreement with numerical results and available experimental data as well as empirical formulas. The dimensionless through-plane permeability is positively correlated with the porosity and negatively correlated with the fractal dimensions for pore and tortuosity at certain porosity.