We　analyze　the　structure　of　the　Faddeev-Jackiw　method　and　show　that　the　canonical　2-form　of　the　Lagrangian　constructed　in　the　last　step　of　the　Faddeev-Jackiw　method　is　always　nondegenerate.　So　according　to　the　Darboux　theorem,　there　must　exist　a　coordinate　transformation　that　can　transform　the　Lagrangian　into　a　standard　form.　We　take　the　coordinates　after　the　transformation　as　these　in　a　phase　space,　and　use　this　standard　form　of　the　Lagrangian,　we　achieve　its　path　integral　expression　over　the　symplectic　space,　give　the　Faddeev-Jackiw　canonical　quantization　of　the　path　integral,　and　then　we　further　show　up　the　concrete　application　of　the　Faddeev-Jackiw　canonical　quantization　of　the　path　integral.