In　this　paper,　the　Nth-order　rogue　waves　are　investigated　for　an　inhomogeneous　higher-order　nonlinear　Schrodinger　equation.　Based　on　the　Heisenberg　ferromagnetic　spin　system,　the　higher-order　nonlinear　Schrodinger　equation　is　generated.　The　generalized　Darboux　transformation　is　constructed　by　the　Darboux　matrix.　The　solutions　of　the　Nth-order　rogue　waves　are　given　in　terms　of　a　recursive　formula.　There　are　complex　nonlinear　phenomena　in　the　rogue　waves,　add　the　first-order　to　the　fourth-order　rogue　waves　are　discussed　in　some　figures　obtained　by　analytical　solutions.　It　is　shown　that　the　general　Nth-order　rogue　waves　contain　free　parameters.　The　free　parameters　play　a　crucial　role　to　affect　the　dynamic　distributions　of　the　rogue　waves.　The　results　obtained　in　this　paper　will　be　useful　to　understand　the　generation　mechanism　of　the　rogue　wave.