The　degenerate　Bogdanov-Takens　system　x　=　y-(a1x+a2x3),　y　=　a3x　+　a4x3　has　two　normal　forms,　one　of　which　is　investigated　in　[Disc.　Cont.　Dyn.　Syst.　B　(22)2017,　1273-1293]　and　global　behavior　is　analyzed　for　general　parameters.　To　continue　this　work,　in　this　paper　we　study　the　other　normal　form　and　perform　all　global　phase　portraits　on　the　Poincaré　disc.　Since　the　parameters　are　not　restricted　to　be　sufficiently　small,　some　classic　bifurcation　methods　for　small　parameters,　such　as　the　Melnikov　method,　are　no　longer　valid.　We　find　necessary　and　sufficient　conditions　for　existences　of　limit　cycles　and　homoclinic　loops　respectively　by　constructing　a　distance　function　among　orbits　on　the　vertical　isocline　curve　and　further　give　the　number　of　limit　cycles　for　parameters　in　different　regions.　Finally　we　not　only　give　the　global　bifurcation　diagram,　where　global　existences　and　monotonicities　of　the　homoclinic　bifurcation　curve　and　the　double　limit　cycle　bifurcation　curve　are　proved,　but　also　classify　all　global　phase　portraits.　©　2018　American　Institute　of　Mathematical　Sciences.　All　Rights　Reserved.