The geometrical and topological configurations of particles have great influences on their surrounding pore tortuosity and the permeability of granular‐porous media. In this work, we develop a relaxation iteration scheme to create random dense packings of different anisotropic‐shaped spheroidal particles with monodispersity and polydispersity in sizes, which manifest the effects of particle shape, fineness, and size distribution on the random packing fraction of particles. Subsequently, we propose a direction‐guided rapidly exploring random tree (DGRRT) algorithm to probe the geometrical tortuosity of complex pore space interstitial to spheroidal particles. A non‐linear pore tortuosity prediction model that relies on the specific surface area and packing fraction of particles, is developed to suit for polydisperse and monodisperse spheroidal particle systems. We further investigate the permeability of granular‐porous media through the lattice Boltzmann method (LBM) of fluid flow. These proposed methods can accurately predict the tortuosity and permeability by comparing against available experimental, theoretical, and numerical results reported in literature. Moreover, the effects of particle packing fraction (i.e., porosity), shape, fineness, and size distribution on the pore tortuosity and permeability of granular‐porous media are evaluated. The results reveal that these microstructural configurations have important influences on the permeability and tortuosity. Our results give an intrinsic interplay between the geometrical tortuosity and permeability of monodisperse and polydisperse particle systems, which have implications for a broad range of scientific disciplines, including the properties of rocks, sandstones and soils, and the design of ultra‐high performance concrete.