In　this　study　we　propose　a　novel　adaptive　finite　element　method　for　the　ground　state　solution　of　Bose-Einstein　Condensates　(BEC).　Different　from　the　classical　adaptive　scheme　applied　to　BEC　which　needs　to　solve　a　nonlinear　eigenvalue　model　directly　on　each　adaptive　finite　element　space,　our　scheme　requires　to　solve　a　linear　elliptic　boundary　value　problem　on　current　adaptive　space　and　a　nonlinear　eigenvalue　model　on　a　quite　low-dimensional　correction　space.　Further,　the　linear　elliptic　boundary　value　problem　is　solved　by　adaptive　multigrid　iterations.　Since　there　is　no　nonlinear　eigenvalue　model　to　be　solved　directly　on　the　adaptive　spaces,　the　solving　efficiency　can　be　improved　evidently.　In　addition,　the　convergence　analysis　of　the　proposed　adaptive　algorithm　are　derived　numerically　and　theoretically.　(C)　2020　Elsevier　Inc.　All　rights　reserved.