Dominance　relation　is　a　stochastic　order,　which　is　an　important　issue　in　modern　finance　research.　In　this　paper,　the　characterizing　of　CR　stochastic　dominance　is　investigated　under　the　framework　of　rank　dependent　expected　utility　(RDEU).　For　a　special　kind　of　distorted　probability　function,　the　investor　with　RDEU　preference　will　unambiguously　reduce　their　optimal　holding　on　the　risky　asset,　when　the　probability　distribution　of　the　risky　asset　become　worse　on　meaning　of　the　first-order　and　CR　stochastic　dominance.　As　a　result,　the　conclusions　of　Gollier　under　the　framework　of　expected　utility　(EU)　are　extended　to　the　RDEU　framework.　©　2018　Walter　de　Gruyter　GmbH.　All　rights　reserved.