The transfer function for an input–output aquifer system has often been used for regional groundwater studies as it allows the simulation of the system response to any varying input at any time resolution. The existing transfer function models available in the literature are limited to dealing with the temporal stationary random input and output flow fields. The stochastic nature of temporal nonstationary inflow-outflow processes is ignored. The present research is therefore devoted to generalizing the previous result by considering the effect of nonstationary inflow-outflow processes of the unconfined aquifer system. It is shown that a closed-form expression for the transfer function can be obtained using the Fourier-Stieltjes representation approach and the representation theorem. The effects of the controlling parameters in the models on the transfer function are analyzed. An application of the present stochastic theory to the prediction of the outflow discharge is demonstrated. The proposed transfer function model should have potential for the analysis of the influence of climate fluctuations on the variation of the aquifer discharge.