  We successfully exhaust the complete set of exact solutions of non-Abelian
vortices in a quiver gauge theory, that is, the S[U(N) x U(N)] gauge theory
with a bi-fudamental scalar field on a hyperbolic plane with a certain
curvature, from SO(3)-invariant SU(2N) Yang-Mills instanton solutions. This
work provides, for the first time, exact non-Abelian vortex solutions. We
establish the ADHM construction for non-Abelian vortices and identify all the
moduli parameters and the complete moduli space.
