In this paper, using numerical modelling, we study Self-Potential (SP) responses of a pumping well partially penetrated an aquifer. We considered short well screens located at different depth and we compare the self-potential responses to those obtained for the well fully penetrated an aquifer, which we served as the reference model. For the case of insulating casing of the pumping well we obtained the results very similar to the reference case and we show the low sensitivity of the SP signals to the drawdown variation. In contrast, for the case of conducting well casing the SP signals increase with the drawdown. For the reference model, a linear relationship between the SP signals and the drawdown was obtained. However, for the short well filters the relationship between the drawdown and the SP signals is logarithmic. We recommend the logarithmic relationship to predict the drawdown values based on SP signals.