In this paper, we first introduced the concepts of FI-cotorsion modules and Strongly FI-torsion free modules and hence, study the behavior of them over FI-Gorenstein ring. For example, we first proved every strongly FI-cotorsion left R-module M is Gorenstein FI-injective over an FI-Gorenstein ring R and secondly, we proved over a right Noetherian ring R with Finite FI-injective dimension of R, then, a left R-module is FI-injective if it is strongly FI-cotorsion with finite FI-flat dimension. Finally, we provided a proof that a left R-module M is Gorenstein FI-injective if and only if it is strongly FI-cotorsion and also proved that a right R-module N is Gorenstein FI-flat if and only if it is strongly FI-torsion free over a FI-Gorenstein ring R with the FI-injective envelope of R is FI-flat. © Rushing Water Publishers Ltd. 2017.