This study is using the multiple relaxation time Lattice Boltzmann method to calculate the permeability of carbon fiber paper and carbon fiber cloth gas diffusion layers (GDL). The 3D gas diffusion layers are generated by X-ray computed tomography, This method involve generation of 3D digital model of gas diffusion layers acquired through X-ray micro-tomography at resolution of a few micros. The reconstructed 3D images were then read into the LBM model to calculate the anisotropic permeability of carbon fiber paper and carbon fiber cloth GDL. We investigated the relationships between the anisotropic permeability and porosity and compare the difference between the two different kinds of GDLs when they have the similar porosity. We also calculate the permeability with different viscosity and compare the two results from the carbon fiber paper and carbon fiber cloth. It is useful for selection of materials for high performance gas diffusion media and can improve the performance of the fuel cells.