  We derive non-Abelian localization formulae for supersymmetric
Yang-Mills-Chern-Simons theory with matters on a Seifert manifold M, which is
the three-dimensional space of a circle bundle over a two-dimensional Riemann
surface \Sigma, by using the cohomological approach introduced by Kallen. We
find that the partition function and the vev of the supersymmetric Wilson loop
reduces to a finite dimensional integral and summation over classical flux
configurations labeled by discrete integers. We also find the partition
function reduces further to just a discrete sum over integers in some cases,
and evaluate the supersymmetric index (Witten index) exactly on S^1x\Sigma. The
index completely agrees with the previous prediction from field theory and
branes. We discuss a vacuum structure of the ABJM theory deduced from the
localization.
