A theoretical model has been proposed and applied to explain recent experimental results concerning the external electric field effect on fluorescence quenching due to intramolecular electron transfer in donor-acceptor pairs linked by a spacer. These results show that for some systems with a short length of a spacer and for a very low concentration of donor-acceptor pairs, the fluorescence quenching of the photoexcited donor is reduced by the electric field instead of being enhanced. The model predicts that the reducing effect of the external electric field on the fluorescence quenching alternates with the enhancing effect when the standard free energy change or the donor-acceptor separation is varied. For systems with a high concentration of the donor-acceptor pairs the resultant effect of the field is determined additionally by competition between the intramolecular and intermolecular electron transfers.