A　new　type　of　adaptive　multigrid　method　is　presented　for　multiple　eigenvalue　problems　based　on　multilevel　correction　scheme　and　adaptive　multigrid　method.　Different　from　the　classical　adaptive　finite　element　method　which　requires　to　solve　eigenvalue　problems　on　the　adaptively　refined　triangulations,　with　our　approach　we　just　need　to　solve　several　linear　boundary　value　problems　in　the　current　refined　space　and　an　eigenvalue　problem　in　a　very　low　dimensional　space.　Further,　the　involved　boundary　value　problems　are　solved　by　an　adaptive　multigrid　iteration.　Since　there　is　no　eigenvalue　problem　to　be　solved　on　the　refined　triangulations,　which　is　quite　time-consuming,　the　proposed　method　can　achieve　the　same　efficiency　as　that　of　the　adaptive　multigrid　method　for　the　associated　linear　boundary　value　problems.　Besides,　the　corresponding　convergence　and　optimal　complexity　are　verified　theoretically　and　demonstrated　numerically.　(C)　2022　Elsevier　B.V.　All　rights　reserved.