Based　on　Finite　Linear　Heat　Theory,　through　Virtual　Source　Method　and　Green　Function　Method,　in　the　whole　area　of　double-boreholes　vertical　U-shape　pipe,　the　heat　transfer　model　outside　boreholes　in　the　cylindrical　coordinate　is　established,　and　the　analytical　solution　of　g-function　and　its　modified　form　are　obtained.　Using　MATLAB,　the　g-function　curve　is　plotted　and　the　soil　temperature　field　is　simulated　and　analyzed　in　case　that　the　Ground　Source　Heat　Exchanger　works　in　cooling　mode.　In　the　end,　the　double-boreholes　heat　transfer　process　is　simulated　by　PDE　toolbox　to　verify　the　accuracy　of　the　model.