Stark shifts are calculated for the ground and first excited electron energy levels in single GaAs/Al_0.35Ga_0.65As quantum wells with non-abrupt interfaces, which is a more appropriate picture for actual samples. The quantum-confined Stark shift for the ground-state electron energy level decreases as the non-abrupt interfaces become larger, but it is always negative. In striking contrast with this behaviour, the existence of non-abrupt interfaces can change the sign of the quantum-confined Stark shift for the first excited energy level in comparison to that calculated considering abrupt interfaces. These effects are shown to be stronger in the case of symmetric rather than asymmetric non-abrupt interfaces.