In　this　paper,　a　type　of　accurate　a　posteriori　error　estimator　is　proposed　for　the　Steklov　eigenvalue　problem　based　on　the　complementary　approach,　which　provides　an　asymptotic　exact　estimate　for　the　approximate　eigenpair.　Besides,　we　design　a　type　of　cascadic　adaptive　finite　element　method　for　the　Steklov　eigenvalue　problem　based　on　the　proposed　a　posteriori　error　estimator.　In　this　new　cascadic　adaptive　scheme,　instead　of　solving　the　Steklov　eigenvalue　problem　in　each　adaptive　space　directly,　we　only　need　to　do　some　smoothing　steps　for　linearized　boundary　value　problems　on　a　series　of　adaptive　spaces　and　solve　some　Steklov　eigenvalue　problems　on　a　low　dimensional　space.　Furthermore,　the　proposed　a　posteriori　error　estimator　provides　the　way　to　refine　mesh　and　control　the　number　of　smoothing　steps　for　the　cascadic　adaptive　method.　Some　numerical　examples　are　presented　to　validate　the　efficiency　of　the　algorithm　in　this　paper.