This　paper　aims　to　introduce　an　asymptotically　exact　a　posteriori　error　estimator　for　non-selfadjoint　Steklov　eigenvalue　problem　arising　from　inverse　scattering　by　using　the　complementary　technique,　which　provides　an　asymptotically　exact　estimate　for　eigenpair　of　non-selfadjoint　Steklov　eigenvalue　problem.　Besides,　as　its　applications,　we　design　a　novel　cascadic　adaptive　method　for　non-selfadjoint　Steklov　eigenvalue　problem　based　on　the　asymptotically　exact　estimate.　In　our　novel　algorithm,　we　will　transform　the　non-selfadjoint　Steklov　eigenvalue　problem　into　some　boundary　value　problems　on　the　adaptive　space　sequence　and　some　non-selfadjoint　Steklov　eigenvalue　problem　on　a　low　dimensional　finite　element　space.　The　involved　boundary　value　problems　are　solved　by　executing　some　smoothing　steps　which　is　the　key　point　of　cascadic　algorithm.　The　mesh　refinement　strategy　and　the　number　of　smoothing　steps　for　the　cascadic　adaptive　method　will　be　controlled　by　the　proposed　asymptotically　exact　a　posteriori　error　estimator.　(C)　2020　IMACS.　Published　by　Elsevier　B.V.　All　rights　reserved.