The temperature response of geothermal heat exchangers (GHEs) can be described more accurately with heat transfer model with groundwater advection. Considering that the current analytical solution model is time-consuming in calculation, a new form of analytical solution of g-function was proposed, and the influence of groundwater flow on the heat transfer in GHEs was discussed. Computations indicate that the calculation efficiency of the new g-function has improved significantly while the reasonable accuracy is maintained, and the value of middle point temperature g-function is larger than that of integral mean temperature g-function. Groundwater advection can improve the effectiveness of GHEs significantly for the step heating flux. The temperature distribution of borehole area is influenced greatly by the arrangement of multiple boreholes.