In this paper first we define the notions of fuzzy prime and fuzzy prime dual ideals in a BCK-algebra. Then we state and prove some related theorems on these notions. By an example we show that the product of two fuzzy prime dual ideals is not necessarily prime. However it is true under some conditions. Then by introducing some new fuzzy subsets extracted from a given fuzzy subset, we give some theorems which show the relation between the structures of these extracted fuzzy subsets and its original fuzzy subset. Finally we give some equivalent conditions of fuzzy prime dual ideals in a BCK-algebra.