  Volume of moduli space of non-Abelian BPS domain-walls is exactly obtained in
U(N_c) gauge theory with N_f matters. The volume of the moduli space is
formulated, without an explicit metric, by a path integral under constraints on
BPS equations. The path integral over fields reduces to a finite dimensional
contour integral by a localization mechanism. Our volume formula satisfies a
Seiberg like duality between moduli spaces of the U(N_c) and U(N_f-N_c)
non-Abelian BPS domain-walls in a strong coupling region. We also find a
T-duality between domain-walls and vortices on a cylinder. The moduli space
volume of non-Abelian local (N_c=N_f) vortices on the cylinder agrees exactly
with that on a sphere. The volume formula reveals various geometrical
properties of the moduli space.
