Abstract: Firstly, we introduce the notion of Gorenstein strongly FP-injective modules by means of acyclic complexes of injective modules and the theory of  Hom functors. Secondly, we study homological properties of Gorenstein strongly FP-injective modules  by using the Horseshoe Lemma and the method of constructing pull-back diagrams, and prove that the class GSFI of Gorenstein strongly FP-injective modules is injectively resolving, with respect to closed under arbitrary direct products and direct summands, and if the Gorenstein strongly FP-injective dimension is finite for every R-module, then (^⊥GSFI, GSFI) forms a complete hereditary cotorsion pair.

Key words: strongly FP-injective module, Gorenstein strongly FP-injective module, cotorsion pair