Laboratory model experiments can be used to verify the applicability and accuracy of a new hydrogeological test method. The unsteady-flow pumping test is the most commonly used comparison method. The axisymmetrical circular aquifer model is frequently used in laboratory model experiments. However, the scale of the laboratory experiment model is always finite, which increases the influence on the test calculation results when using conventional Theis theory. Here, based on analytical analysis and laboratory experiments, a new calculation method is proposed for the circular constant water-head boundary of finite scale. The proposed method can eliminate the effect of the finite-scale circular constant water-head boundary on the unsteady pumping test results and can also be applied to large-scale circular constant water-head boundaries. Geotextiles are permeable fabrics; therefore, the hydraulic conductivity of a geotextile can be used to simulate the hydraulic conductivity of a fractured aquifer. A geotextile test, steady pumping test and slug test were conducted to verify the accuracy of the proposed calculation method, with all the results indicating that the proposed method can provide more accurate hydrogeological parameters from an unsteady pumping test with a circular constant water-head boundary of finite scale than conventional Theis theory for unsteady pumping tests.