In　this　paper,　we　propose　a　type　of　adaptive　multigrid　method　for　eigenvalue　problem　based　on　the　multilevel　correction　method　and　adaptive　multigrid　method.　Different　from　the　standard　adaptive　finite　element　method　applied　to　eigenvalue　problem,　with　our　method　we　only　need　to　solve　a　linear　boundary　value　problem　on　each　adaptive　space　and　then　correct　the　approximate　solution　by　solving　a　low　dimensional　eigenvalue　problem.　Further,　the　involved　boundary　value　problems　are　solved　by　some　adaptive　multigrid　iteration　steps.　The　proposed　adaptive　algorithm　can　reach　the　same　accuracy　as　the　standard　adaptive　finite　element　method　for　eigenvalue　problem　but　evidently　reduces　the　computational　work.　In　addition,　the　corresponding　convergence　and　optimal　complexity　analysis　are　derived　theoretically　and　numerically,　respectively.