A　new　symplectic　Lagrangian　density　and　Faddeev-Jackiw　(FJ)　generalized　brackets　of　the　gauge　invariant　self-dual　fields　interacting　with　gauge　fields　have　been　obtained　and　FJ　quantization　of　this　system　has　been　presented.　Furthermore,　the　FJ　method　is　compared　with　Dirac　method　and　the　results　indicate　that　the　two　methods　are　equivalent　in　the　quantization　of　this　system.　After　analyzing,　it　can　be　found　in　this　paper　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　the　first-　and　the　second-class　constraints.　Therefore,　the　FJ　method　is　a　more　economical　and　effective　method　of　quantization.