The dynamics of two-phase flows with a constant driving force inside a micro-channel is studied by using the Lattice Boltzmann Method (LBM) and the Shan-Chen multiphase model in this article.Flow regimes under different wall wettabilities and over smooth and grooved geometric surfaces are investigated.It is found that flow behaviors are strongly affected by the wall wettability and topography.Our results show that the LBM is efficient and accurate,and has very good application prospect in the study of drag reduction of microscopic seepage of reservoir.