In　this　paper,　based　on　the　model　of　Zhao,　Qin,　and　Chen　[Adv.　Differ.　Equ.　2018:172,　2018],　we　propose　a　new　model　of　the　May　cooperative　system　with　strong　and　weak　cooperative　partners.　The　model　overcomes　the　drawback　of　the　corresponding　model　of　Zhao,　Qin,　and　Chen.　By　using　the　differential　inequality　theory,　a　set　of　sufficient　conditions　that　ensure　the　permanence　of　the　system　are　obtained.　By　combining　the　differential　inequality　theory　and　the　iterative　method,　a　set　of　sufficient　conditions　that　ensure　the　extinction　of　the　weak　partners　and　the　attractivity　of　the　strong　partners　and　the　other　species　is　obtained.　Numeric　simulations　show　that　too　large　transform　rate　will　lead　to　more　complicated　fluctuation;　however,　the　system　is　still　permanent.　©　2020,　The　Author(s).