Аннотация:Using the new limit on the neutrino anomalous magnetic moment recently obtained by the GEMMA experiment on measurements of the cross-section for the reactor antineutrino scattering on free electrons, we get, by comparing the neutrino magnetic moment and millicharge contributions to the total cross-section at the electron recoil energy threshold of the experiment, an order-of-magnitude estimation for a possible new direct upper bound on the neutrino electric millicharge ∣qν∣∼1.5×10−12e0 (e(0) is the absolute value of the electron charge). This estimation is confirmed by the performed analysis of the GEMMA data using established statistical procedures and a new direct bound on the neutrino millicharge absolute value ∣qν∣<2.7×10−12e0 (90% C.L.) is derived. This limit is more stringent than the previous one obtained from the TEXONO reactor experiment data that is included to the Review of Particle Properties 2012. We also predict, in an order-of-magnitude estimation, that with data from the ongoing new phase of the GEMMA experiment (GEMMA-II) the upper bound on the neutrino millicharge will reach an expected level of about ∣qν∣∼3.7×10−13e0 within two years. We also predict that, with the next phase of the considered experiment (GEMMA-III), the upper bound on the millicharge will be reduced by an order of magnitude over the present bound and reach the level ∣qν∣∼1.8×10−13e0 within approximately four years.