The lattice gas automation (LGA) simulations for electrical transport properties have been performed on digital rock samples virtually saturated with oil and water to investigate the relationship between resistivity index and water (oil) saturation (I–Sw) of reservoir rocks at micropore scale. The digital rocks were constructed by the pileup of matrix grains with a radius distribution obtained by laboratory measurements on reservoir rock samples. The LGA was then applied to simulate the flow of electrical current through the pores of these virtually saturated digital rocks to reveal the non-Archie relation of I–Sw. The results from LGA simulation indicate that the I–Sw relation is generally a non-linear function changing with the decrease of water saturation and porosity on a log–log scale. Archie's equation is an approximation in high water saturation range. Based on this study, we developed a new equation for non-Archie relation of I–Sw to improve the calculation of pore fluid saturation. The calculated results with this new equation have shown better fit to laboratory measurements.