A　logistic　model　with　impulsive　Holling　type-II　harvesting　is　proposed　and　investigated　in　this　paper.　Here,　the　species　is　harvested　at　fixed　moments.　By　using　the　techniques　derived　from　the　theory　of　impulsive　differential　equations,　sufficient　conditions　for　both　permanence　and　extinction　of　the　system　are　established,　respectively.　Sufficient　conditions　which　ensure　the　existence,　uniqueness,　and　global　attractivity　of　a　positive　periodic　solution　of　the　system　are　obtained.　Our　study　shows　that　impulsive　controls　play　an　important　role　in　maintaining　the　sustainable　development　of　the　ecological　system.　Compared　with　the　linear　impulsive　capture　or　continuous　nonlinear-type　capture,　our　study　shows　that　the　nonlinear　impulsive　capture　could　lead　to　more　complicated　dynamic　behaviors.　Numeric　simulations　are　carried　out　to　show　the　feasibility　of　the　main　results.　The　results　obtained　here　maybe　useful　to　the　practical　biological　economics　management.　©　2018,　The　Author(s).