In　this　paper,　a　new　type　of　adaptive　finite　element　method　is　proposed　for　nonlinear　eigenvalue　problems　in　electronic　structure　calculations　based　on　the　multilevel　correction　method　and　adaptive　multigrid　method.　Different　from　the　classical　adaptive　finite　element　method　for　electronic　structure　calculations　which　needs　to　solve　a　nonlinear　eigenvalue　model　directly　in　each　adaptive　finite　element　space,　our　approach　only　needs　to　solve　a　linear　elliptic　boundary　value　problem　by　adaptive　multigrid　method　in　each　adaptive　space,　and　then　correct　the　eigenpair　approximation　by　solving　a　small-scale　nonlinear　eigenvalue　model　in　a　low-dimensional　correction　space.　Since　solving　large-scale　nonlinear　eigenvalue　model　is　avoided　which　has　exponentially　increased　computational　time,　the　efficiency　of　electronic　structure　calculations　can　be　improved　evidently.　In　addition,　the　corresponding　convergence　analysis　of　the　proposed　adaptive　multigrid　algorithm　are　also　derived　theoretically　and　numerically.　©　2023　Elsevier　B.V.