Artificial recharge is an effective remediation measure for controlling groundwater level and subsidence in many coastal cities in China. Hydraulic parameters estimated by pumping tests are often used in the design of both pumping and recharge systems. However, the hydraulic parameters in the recharge process have been found to differ from those in the pumping process and should be studied in greater detail. Eight single-well pumping and recharge tests were conducted within a confined aquifer in a soft soil area in the city of Tianjin, and the differences in wellbore storage influences and well losses between the recharge and pumping processes were examined. Furthermore, based on the Hantush and Jacob model, an algorithm combining the Levenberg–Marquardt algorithm (LMA) and genetic algorithm (GA) was employed for estimation of the hydraulic parameters. The results illustrated that the combined algorithm eliminating wellbore storage influences could provide hydraulic parameters from which the groundwater level variation could be accurately simulated. The hydraulic conductivity and specific storage values obtained in the pumping tests were higher than those obtained in the recharge tests. In addition to slight plugging of the recharge well, the specific storage differences could be explained by the compression and rebound deformation characteristics of sand in the confined aquifer. The specific storage estimated by pumping tests should be adjusted when applied in groundwater recharge calculation.