  We study the Chern-Simons $CP(N)$ models with a global $U(1)$ symmetry and
found the self-dual models among them. The Bogomolnyi-type bound in these
self-dual models is a nontrivial generalization of that in the pure $CP(N)$
models. Our models have quite a rich vacuum and soliton structure and approach
the many known gauged self-dual models in some limit.
