A　discrete　May　type　cooperative　model　incorporating　Michaelis-Menten　type　harvesting　takes　the　form　is　proposed　and　studied　in　this　paper.　Sufficient　conditions　which　ensure　the　permanence,　extinction　of　the　first　species　and　the　existence　of　a　unique　globally　attractive　interior　equilibrium　of　the　system　are　obtained,　respectively.　Numeric　simulations　are　carried　out　to　show　the　feasibility　of　the　main　results.　©　2020　International　Association　of　Engineers.