In　this　paper,　a　type　of　full　multigrid　method　is　proposed　to　solve　non-selfadjoint　Steklov　eigenvalue　problems.　Multigrid　iterations　for　corresponding　selfadjoint　and　positive　definite　boundary　value　problems　generate　proper　iterate　solutions　that　are　subsequently　added　to　the　coarsest　finite　element　space　in　order　to　improve　approximate　eigenpairs　on　the　current　mesh.　Based　on　this　full　multigrid,　we　propose　a　new　type　of　adaptive　finite　element　method　for　non-selfadjoint　Steklov　eigenvalue　problems.　We　prove　that　the　computational　work　of　these　new　schemes　are　almost　optimal,　the　same　as　solving　the　corresponding　positive　definite　selfadjoint　boundary　value　problems.　In　this　case,　these　type　of　iteration　schemes　certainly　improve　the　overfull　efficiency　of　solving　the　non-selfadjoint　Steklov　eigenvalue　problem.　Some　numerical　examples　are　provided　to　validate　the　theoretical　results　and　the　efficiency　of　this　proposed　scheme.