Abstract: We consider Gorenstein FP-injective complexes, firstly, we  prove that  a complex G is Gorenstein FP-injective if and only if there is an exact sequence …→E^-1→E⁰→E¹→E²→… of FP-injective complexes with G=Ker(E⁰→E¹) on coherent rings. Secondly, we  prove that  a complex G is Gorenstein FP-injective if and only if G_m is a Gorenstein FP-injective module for each m∈Z under certain conditions.

Key words: Gorenstein FP-injective complex, Gorenstein FP-injective module, coherent ring