Pore structure of porous media, including pore size and topology, is rather complex. In immiscible two-phase displacement process, the capillary force affected by pore size dominates the two-phase flow in the porous media, affecting displacement results. Direct observation of the flow patterns in the porous media is difficult, and therefore knowledge about the two-phase displacement flow is insufficient. In this paper, a two-dimensional (2D) pore structure was extracted from a sandstone sample, and the flow process that CO2 displaces resident brine in the extracted pore structure was simulated using the Navier-Stokes equation combined with the conservative level set method. The simulation results reveal that the pore throat is a crucial factor for determining CO2 displacement process in the porous media. The two-phase meniscuses in each pore throat were in a self-adjusting process. In the displacement process, CO2 preferentially broke through the maximum pore throat. Before breaking through the maximum pore throat, the pressure of CO2 continually increased, and the curvature and position of two-phase interfaces in the other pore throats adjusted accordingly. Once the maximum pore throat was broken through by the CO2, the capillary force in the other pore throats released accordingly; subsequently, the interfaces withdrew under the effect of capillary fore, preparing for breaking through the next pore throat. Therefore, the two-phase displacement in CO2 injection is accompanied by the breaking through and adjusting of the two-phase interfaces.