  In this paper we establish the existence of multi-vortices for a generalized
self-dual Chern--Simons model. Doubly periodic vortices, topological and
non-topological vortex solutions are constructed for this model. For the
existence of doubly periodic vortex solutions, we establish an explicitly
necessary and sufficient condition. It is difficult to get topological
multi-vortex solutions due to the non-canonical structure of the equations. We
overcome this difficulty by constructing a suitable sub-solution for the
reduced equation. This technique maybe applied to the problems with similar
structures. For the existence of non-topological solutions we use a shooting
argument.
