Supercritical carbon dioxide (SC-CO2) fracturing is a promising technology for unconventional energy development and carbon capture and storage. Experimental studies have shown that (SC-CO2 fracturing can form complex fracture networks and reduce crack initiation pressure, which are different results from those when fracturing with aqueous fluids. The complex fracture networks that form from SC-CO2 fracturing may be the result of strong seepage effects (i.e., low capillary and viscous forces). To understand the different injection behaviors induced by (SC-CO2 and aqueous fluids in low-permeability rocks, this study develops a new two-phase steady-state model based on the pore-scale network method. Although other models consider the viscous force, our model implements the capillary and viscous forces to reproduce the seepage effect. Because of the capillary force, the flow model is nonlinear and solved by iteratively solving matrix equations until a conservation of volumetric flux is satisfied. Simulation results show that the capillary force in a two-phase flow system in small pore spaces has consequential effects on its pressure distribution. Such factors lead to discontinuous pressure drops. This study shows that the seepage effect of (SC-CO2 is stronger than that of aqueous fluids and can largely avoid the capillary blockage that arises in oil-water systems.