In this paper, we consider the notion of semiprime submodules, which is a natural generation of semiprime ideals. The main purpose of this paper is to give local-global properties of semiprimes and semiprime radicals as well as results on finitely generated multiplication modules. Also, we prove that for every submodule of a module , the semiprime radical of in is the direct limit of the ascending chain of submodules of , and we prove that satisfies the semiprime radical formula if and only if its envelope in is semiprime.