The Lattice Gas Automation (LGA) method, which is improved by introducing a reflection coefficient for the border between phases to show its effect on current path, is used in this paper to simulate the current flow in digital rock for investigating the effects of clay content and clay distribution types on the relationship between formation factor(F) and rock porosity(φ). The digital rock model is constructed by simulating a natural deposit of matrix particles with different shapes and radius. Based on the simulation results, it was found that both dispersed clay and laminated clay can lead to a non-Archie relationship of F-φ. The non-Archie effect of laminated clay on the F-φ relationship was more significant than that of dispersed clay. Moreover, a realistic model is developed in this work for quantitatively describing the effect of clay content (Denoted as Vsh) on parameters a and m. These study results have further demonstrated the validity of LGA in study of electrical transport properties at a pore scale.