Our previous study (Song et al., 2018) proposed a novel enhanced geothermal system (EGS) with multilateral wells and demonstrated that it had greater heat extraction performance than double-well EGS. However, to further enhance the heat extraction performance of multilateral-well EGS, an efficient and complex fracture network needs to be created to connect injection and production wells. In order to know which kind of discrete fracture network (DFN) should be created to improve the heat extraction performance of multilateral-well EGS, it is extremely important to investigate effects of DFN on multilateral-well EGS performance. Therefore, in this study, we develop a thermal-hydraulic-mechanical (THM) coupling model to investigate the heat extraction performances of various DFNs. The model is verified by an analytical solution. Based on the model, effects of rock mechanical behavior on fracture permeability evolution and EGS heat extraction performance are studied. The sensitivity analysis of reservoir properties and injection temperature on THM coupling process are conducted. Influences of fracture parameters, including number of fractures, fracture length and orientation, on multilateral-well EGS performance are investigated. The results indicate that the rock contraction could increase fracture permeability and promote the preferential flow and thermal breakthrough. The injection temperature and reservoir properties have significant effects on the rock deformation and heat extraction performance of multilateral-well EGS. The DFN with complex and longer fractures and without too many direct connections between lateral wells and fractures is beneficial for multilateral-well EGS performance. The results of this study provide significant suggestions for the fracturing operation of multilateral-well EGS.