A new mechanism of electromagnetic radiation by electrons under the influence of a dense neutrino flux, termed "the spin light of electron" in neutrino flux (SLe ν ), is considered. It is shown that in the case when electrons are moving against the neutrino flux with relativistic energy there is a reasonable increase of the efficiency of the energy transfer from the neutrino flux to the electromagnetic radiation by the SLe ν mechanism. The proposed radiation process is applied to an astrophysical environment with characteristics peculiar to supernovae. It is shown that a reasonable portion of energy of the neutrino flux can be transferred by the SLe ν to gamma-rays .