The effect of an electric field E on a narrow quantum ring that contains two electrons and is threaded by a magnetic flux B has been investigated. Localization of the electronic distribution and suppression of the AharonovBohm oscillation (ABO) are found in the two-electron ring, which are similar to those found in a one-electron ring.However, the period of ABO in a two-electron ring is reduced by half compared with that in a one-electron ring.Furthermore, during the variation of B, the persistent current of the ground state may undergo a sudden change in sign.This change is associated with a singlet-triplet transition and has no counterpart in one-electron rings. For a given E,there exists a threshold of energy. When the energy of the excited state exceeds the threshold, the localization would disappear and the ABO would recover. The value of the threshold is proportional to the magnitude of E. Once the threshold is exceeded, the persistent current is much stronger than the current of the ground state at E = 0.