The concepts of cubic JD-Fuzzy Ideals are introduced, & many properties are studied. Their image and their inverse image in BH-algebras are defined & investigated. We’ll refer to BH-algebra by BH-G, fuzzy set by F.S, interval-valued by I.V. & to cubic S. by  cubic S. and we studied the P union of any collection of cubic JD-Fuzzy Ideal and we find is also cubic JD-Fuzzy Ideal, as well as we introduced R union for any given set of cubic JD-Fuzzy Ideal not always be a cubic JD-Fuzzy Ideal, for example. However, we can say A homomorph   pre-image of cubic JD-Fuzzy Ideal is cubic JD-ideal.