  We calculate the emissivity due to neutrino-pair production in $e^+e^-$
annihilation in the context of a left-right symmetric model in a way that can
be used in supernova calculations. We also present some simple estimates which
show that such process can act as an efficient energy-loss mechanism in the
shocked supernova core. We find that the emissivity is dependent of the mixing
angle $\phi$ of the model in the allowed range for this parameter.
