We propose a model potential for computing total ionization cross sections for atoms and molecules by electron impact. The potential is obtained by a fitting procedure using the Binary-Encounter-Bethe model cross sections as a starting point. We present total ionization cross section for hydrogen, carbon, nitrogen and oxygen atoms and for hydrogen, nitrogen, water, methane and benzene molecules. The results obtained with our model potential are compared with results obtained with the Binary-Encounter-Bethe model and with the first Born approximation, and agreement is quite good. Our results show that this potential could be used to account for the ionization channel in an electron-molecule collision calculation.