Large-scale　nonsymmetric　eigenvalue　problems　are　common　in　various　fields　of　science　and　engineering　computing.　However,　their　efficient　handling　is　challenging,　and　research　on　their　solution　algorithms　is　limited.　In　this　study,　a　new　multilevel　correction　adaptive　finite　element　method　is　designed　for　solving　nonsymmetric　eigenvalue　problems　based　on　the　adaptive　refinement　technique　and　multilevel　correction　scheme.　Different　from　the　classical　adaptive　finite　element　method,　which　requires　solving　a　nonsymmetric　eigenvalue　problem　in　each　adaptive　refinement　space,　our　approach　requires　solving　a　symmetric　linear　boundary　value　problem　in　the　current　refined　space　and　a　small-scale　nonsymmetric　eigenvalue　problem　in　an　enriched　correction　space.　Since　it　is　time-consuming　to　solve　a　large-scale　nonsymmetric　eigenvalue　problem　directly　in　adaptive　spaces,　the　proposed　method　can　achieve　nearly　the　same　efficiency　as　the　classical　adaptive　algorithm　when　solving　the　symmetric　linear　boundary　value　problem.　In　addition,　the　corresponding　convergence　and　optimal　complexity　are　verified　theoretically　and　demonstrated　numerically.