The concepts of Cwrpp radical congruences(or sets) and semi-Cwrpp semigroups were introduced.The properties of Cwrpp radical congruence(or set) were studied.It was shown that for left Cwrpp(or right Crpp) and perfect rpp semigroups,their Cwrpp radicals are strong.The characteristics of their Cwrpp radicals were presented and it was proven that a semigroup S is semi-Cwrpp if and only if S is isomorphic to a sub 0-direct product for some Cwrpp semigroups.