Shale is composed of various mineral components: quartz, feldspar, clay, carbonate, organic matter (OM), etc. The imaging technology with nanometer resolution has observed nanometer-scale pore structures in various components. The pore size in OM and clay is generally smaller than that of quartz pores. What’s more, the OM and inorganic minerals show different fluid-solid interactions, leading to the mixed wettability in shale media. The flow and storage characteristics of oil and water in this nanoporous system under mixed wetting conditions are poorly understood. In this study, we establish a multi-component pore-scale model containing quartz, clay, and OM based on pore network modeling. A two-phase flow simulation method considering capillary force and viscous force is developed and used to simulate the process of water injection. We track the dynamic movement of oil/water interfaces, and obtain the distribution of oil and water in different types of pores. Results show that the increase of clay content reduces the displacement efficiency of quartz pores while improves the mobilization of oil in OM. The water saturation in pores with smaller size increases when the clay content is higher. The results of this study help in understanding the flow behavior of oil and water in shale nanoporous system with multiple mineral components.