An intuitionistic fuzzy set A is said to be intuitionistic fuzzy rgα-closed [21] in intuitionistic fuzzy topological spaces if αcl(A) ⊆ U whenever A ⊆ U and U is intuitionistic fuzzy regular α- open in X. In this paper we introduce quasi rgα -open mapping from intuitionistic fuzzy topological space X to intuitionistic fuzzy topological Y as the image of every intuitionistic fuzzy rgα -open set is intuitionistic fuzzy open. Also we obtain its Characterization and basic properties.