In this paper, the concept of fuzzy BCK-submodule is introduced and some properties, related results and equivalent conditions are given. The fuzzy BCK-submodule generated by a fuzzy subset is characterized and then the lattice of fuzzy BCK-submodules of a BCK-module is studied and showed that it is a distributive lattice. Also, some operations of fuzzy BCK-submodules are presented. Next, the concept of fuzzy residual quotient BCK-modules is introduced and some basic properties are obtained. Finally, the concept of a fuzzy multiplication BCK-module is defined and using the concept of fuzzy residual quotient BCK-submodule, some characterizations of it are given.