Let R be a unital ring and M a unitary module not necessary over R. The FGDF-module is a generalization of FGDF-rings (Touré, Diop, Mohamed and Sangharé, 2014). In this work, we first give some properties of FGDF-modules. After that, we show that for a finitely generated module M, M is a FGDF-module if and only if M is of finite representation type module. Finally, we show that M is a finitely generated FGDF-module if and only if every Dedekind finite module of $\sigma[M]$ is noetherian.