  We derive a series of moment equations describing the motion and flavor
transformation of neutrinos in supernova. We find a particular series of
moments of neutrino density matrix in supernova. The emission angle
distribution of neutrinos is described by this series of moments. We expand the
equation of neutrinos using these moments and obtain moment equations. We find
that these moments have very good property of convergence and the infinite
series of equations can be truncated to equations with a small set of moments.
Using a small set of moment equations the required computational power is
reduced by about two orders of magnitude compared to that in multi-angle
simulation. The study on non-linear flavor transformation of neutrinos is
substantially simplified using these equations. Two flavor system of neutrinos
is also considered and new equations describing the flavor polarization vectors
of neutrinos are found.
