The advantages of using supercritical carbon dioxide as working fluid in geothermal development (potential carbon dioxide geological storage and relatively high mobility) have attracted considerable interest in the simulation of a carbon dioxide-based enhanced geothermal system. This study proposed a numerical model based on the three-dimensional unified pipe-network method to simulate the two-phase flow and thermal-hydraulic coupled process in a carbon dioxide-based enhanced geothermal system considering complex fracture networks. The van Genuchten capillary model and relative permeability model are adopted to characterize the displacement process in both the fractures and the rock matrix. A pipe equivalent technique is employed to discretize the governing equations for the two-phase flow and the heat transmission with the local thermal non-equilibrium concept. Two-phase fluid transfer at material interfaces is solved based on a pipe superposition principle in a pipe-network system. Discretized forms are solved by a sequential implicit time scheme alleviating the Courant-Friedrichs-Lewy condition in fracture networks. The proposed model is verified against analytical results for the Buckley-Leverett problem. Saturation evolution curves at different time steps converge to the analytical solutions as the node number increases. Sensitivity analyses using a doublet system horizontally embedded with one large fracture indicate that the capillary contrast between the rock matrix and the fractures and the injection flow rate pose impacts on the produced carbon dioxide saturation and the outlet fluid temperature drawdown. The simulation of circulating processes considering randomly generated fracture networks demonstrates that the more promising potential of heat extraction can be achieved using the pure carbon dioxide as the working fluid instead of cooled water. Analyzing the effects of the initial reservoir carbon dioxide saturation shows that increasing the reservoir carbon dioxide saturation before heat excavation can improve the heat production. Both increase the matrix permeability and the fracture aperture enhances the performance of the heat extraction and the carbon dioxide sequestration.