The pressure drop in the ceramic filter system of the after-treatment device has a great effect on automobile engine performance. To predict the pressure drop under various operating conditions, it is necessary to analyze how the structural properties of porous media affect the permeability. The commonly used Kozeny-Carman model correlating permeability and porosity is useful for porous media composed of spherical grains, but exhibits considerable deviations in the actual ceramic filter system with low porosity. In this study, the permeability of overlapped-random structured porous media with low porosity was numerically solved by mesoscopic lattice Boltzmann (LB) method in Darcy flow regime. Based on LB simulation results, a new capillary model modified from Kozeny-Carman model is proposed for practically predicting the permeability of complex porous filter systems, using key structural variables such as porosity, tortuosity, and effective pore-throat radius.