In　this　paper,　a　type　of　cascadic　adaptive　finite　element　method　is　proposed　for　eigenvalue　problem　based　on　the　complementary　approach.　In　this　new　scheme,　instead　of　solving　the　eigenvalue　problem　in　each　adaptive　finite　element　space　directly,　we　only　need　to　do　some　smoothing　steps　for　a　boundary　value　problems　on　each　adaptive　space　and　solve　some　eigenvalue　problems　on　a　low　dimensional　space.　Hence　the　efficiency　can　be　improved　since　we　do　not　need　to　solve　the　eigenvalue　problems　on　each　adaptive　space　which　is　time-consuming.　Further,　the　complementary　error　estimate　for　eigenvalue　problem　will　be　introduced.　This　estimate　can　not　only　provide　an　accurate　error　estimate　for　eigenvalue　problem　but　also　provide　the　way　to　refine　mesh　and　control　the　number　of　smoothing　steps　for　the　cascadic　adaptive　algorithm.　Some　numerical　examples　are　presented　to　validate　the　efficiency　of　the　proposed　algorithm　in　this　paper.