  By using $\phi$ -mapping method, we discuss the topological structure of the
self-duality solution in Jackiw-Pi model in terms of gauge potential
decomposition. We set up relationship between Chern-Simons vortices solution
and topological number which is determined by Hopf index and and Brouwer
degree. We also give the quantization of flux in the case. Then, we study the
angular momentum of the vortex, it can be expressed in terms of the flux.
