Comprehensive computational modeling based on a full statistical approach is performed to investigate the heterogeneous multi-transport characteristics in the gas diffusion layers of fuel cells. For the purposes, a series of carbon paper gas diffusion layers are randomly generated at a 95% confidence level to reflect the heterogeneous microstructures. A representative element volume is determined based on the relative porosity gradient errors to minimize the uncertainty in the statistical analysis. Subsequently, a single-phase three-dimensional lattice Boltzmann method is applied to obtain the velocity distribution throughout the porous layers, enabling to calculate the average tortuosity. The effective mass diffusivity in the diffusion layers is then derived from the tortuosity factor. Additionally, three directional permeabilities are derived from the pressure gradient to account for the anisotropic characteristics of the porous diffusion layers. The relationship between the permeability and porosity is found to match the modified Kozeny Carman equations. Further, a path-finding algorithm based on the percolation theory is developed to simulate electron and thermal conduction along the carbon fibers in the in-plane and through-plane directions. The present model can be utilized to investigate the heterogeneous transport characteristics of fibrous porous diffusion media for various electrochemical systems. (C) 2019 Elsevier Ltd. All rights reserved.