A binary mixture lattice Boltzmann model (LBM) is used to simulate the diffusion process in stochastic fractal porous media generated by the fractional Brownian motion model. The isotropic porous media is reconstructed from fractional Brownian rough surface using the random midpoint displacement algorithm and the binary processing. In addition, the 2D and 3D anisotropic porous media is generated by transforming the isotropic fractional Brownian rough surface with a structure filter. LBM is applied to simulate the diffusion processes of reconstructed isotropic and anisotropic porous media for various fractal dimensions. The results indicate that the increasing fractal dimension can lead to the reduction of effective diffusion coefficients at the same porosity. The degrees of anisotropy for diffusion of anisotropic porous media are presented with the different anisotropic strength. (C) 2014 Elsevier Ltd. All rights reserved.