The neutrino-electron scattering has been discussed according to the photon-neutrino weak-coupling theory. The results are then compared with those obtained in the current-current coupling theory. The rate for neutrino-electron scattering has also been discussed for nondegenerate and degenerate gases. Astrophysical applications are then made by evaluating the ratio of the neutrino mean free path to the stellar radius. It is shown that, according to the photon-neutrino weak coupling, the neutrino mean free path exceeds the stellar radius for massive stars, white dwarfs and neutron stars. This result is significant in the sense that according to the current-current coupling theory, the ratio of the neutrino mean free path to the stellar radius for neutron stars can be much less than unity, though for other types of stars the neutrino mean free path exceeds the stellar radius. Finally, some remarks are made about the experiment attempted by Reines and Kropp to detect solar neutrinos using knock-on electrons produced in the neutrino-electron scattering.