Abstract：An approximate solution to the differential equations of axisymmetric unsteady well-flow was derived to assess the water level and discharge based on Boltzmann transformation，which can predict the variation of water level and discharge of a fully penetrating well in the infinite confined aquifer under unsteady well-flow condition caused by fixed-drop pumping. The effect of well diameter was taken into account in the solution. The relative error of the approximate solution to the classical solution is 0–15%，and the approximate solution is simpler and more convenient than the classical method. The applicability of the approximate solution was verified through a case study. The results showed that the approximate solution is identical with data in the case.