In this article, we introduce γ-continuous function which generalises some known continuous functions. Then we introduce some new fuzzy open and closed functions namely fuzzy locally γ-closed function, fuzzy γ-closed function, fuzzyγ-open function, fuzzy (γ,β)-open function and fuzzy (γ,β)-closed function. We also studied some properties of these notions. Keywords: Fuzzy Q-neighbourhood, fuzzy γ-open set, fuzzyγ-continuous function, fuzzy γ-closed set, fuzzy γ-open function, fuzzy γ-closed function, fuzzy (γ,β)-closed function, fuzzy (γ,β)-open function