Understanding the fluid flow and heat transfer process in the well-fracture-reservoir combined system is crucial for the development of Enhanced or Engineered Geothermal Systems (EGS). In this paper, a well-fracture-reservoir integrated numerical model is developed to study the heat extraction performance considering the interactions among the well boreholes, the fractures in the reservoir and the base rock reservoir itself. The wells and major fractures are precisely described by the direct modelling while the sub-fractures in the base rock are described by a permeability distribution. A novel method to improve the heat extraction performance of EGS by enhancing the permeability in the near-well region is proposed. Simulation results show that the fluid flow path is predominantly determined by the well layout and fracture network. The fluid pressure is non-linearly distributed between the injection and production wells in the fractures and reservoir. Further, an optimized scheme for heat extraction of an assumed geothermal site in Gonghe Basin is proposed based on the near-well enhancement approach. The overall heat extraction performance of the near-well enhanced case is improved by more than 15.0%. The present work provides a feasible improvement scheme for EGS to achieve a better heat extraction performance.