In　this　paper,　we　study　a　Lotka-Volterra　prey-predator　system　with　feedback　control.　We　establish　sufficient　conditions　under　which　a　unique　positive　equilibrium　is　globally　stable.　Further,　we　show　that　a　suitable　feedback　control　on　predator　species　can　make　prey　species　that　is　on　the　brink　of　extinction　become　globally　stable,　but　under　the　conditions　of　small　feedback　control　on　predator,　the　prey　species　still　extinct,　whereas　the　predator　species　is　stable　at　certain　values.　Several　examples　are　presented　to　show　the　feasibility　of　the　main　results.　©　2017,　The　Author(s).