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In the classical setting neighborhood structures are the standard semantic tool used for non-normal modal logics. In this paper we introduce a new fuzzy version of this semantics and we prove that it is a natural generalization in the sense that fuzzy Kripke models (see \cite{BoEsGoRo11}) can be identified as a special kind of our proposed models.In addition, we characterize this notion in a syntactic way and describe conditions on fuzzy neighborhood models sufficient for the validation of different and well known schemes. This approach is a fuzzy version of the classicallyknown as the neighborhood semantics and its classical systems %\cite[Chap. 7]{Chellas80}.