  We obtain a new symplectic Lagrangian density and deduce Faddeev-Jackiw (FJ)
generalized brackets of the gauge invariant self-dual fields interacting with
gauge fields. We further give FJ quantization of this system. Furthermore, the
FJ method is compared with Dirac method, the results show the two methods are
equivalent in the quantization of this system. And by the practical research in
this letter, it can be found that the FJ method is really simpler than the
Dirac method, namely, the FJ method obviates the need to distinguish primary
and secondary constraints and first- and second-class constraints. Therefore,
the FJ method is a more economical and effective method of quantization.
