Ideals is one of the important tools for studying the structure characteristics of logical algebras. In this paper, by using methods and principles of algebra and fuzzy sets, we introduce the notion of fuzzy $LI$-ideals and investigate their properties in bounded Heyting algebras. Relation between fuzzy $LI$-ideals and fuzzy lattice ideals is also discussed. Representation theorem of fuzzy $LI$-ideal generated by a fuzzy set is provided. Furthermore, we prove that the set consisting of all fuzzy $LI$-ideals in a given bounded Heyting algebra, under fuzzy set-inclusion order, forms a complete Heyting algebra.