We introduce the notion of normal fuzzy BCC-ideals, maximal fuzzy BCC-ideal and completely normal fuzzy BCC-ideal in BCC-algebras. We investigate some properties of normal (resp. maximal, completely normal) BCC-ideals. We show that for every non-constant normal fuzzy BCC-ideal which is a maximal element of $(N(X), \subsetq)$ takes only the values 0 and 1, and every maximal fuzzy BCC-ideal is completely normal.