Let R be a commutative ring with identity and M a unital R-module. The module M is said to be a multiplication module provided for each submodule N of M there exists an ideal I of R such that N=IM. It is clear that every cyclic R-module is a multiplication module. Let End(M) be the ring of R-homomorphisms of M. An endomorphism r.p of M will be called trivial if there exists a E R such that r.p(m) = am for all m E M. W. Vasconcelos[8] proved that for a commutative ring R, injective endomorphisms of finitely generated R-modules are isomorphisms if and only if every prime ideal of R is maximal. Also, J. Strooker[7] and Vasconcelos[8] independently proved that for a commutative ring R, surjective endomorphisms of finitely generated Rmodules are isomorphisms. In this paper, We relate these concepts to multiplication module terminology. Also we will show that if M is a finitely generated multiplication module, then every endomorphism of M is trivial (See Theorem 3) and some other related properties of endomorphisms of multiplication modules are studied.