Summary: In this paper, the notions of FI-gr-injective modules and strongly FI-gr-injective modules are introduced, and the relationship between them and graded injective modules is explained. It is proved that the graded ring \(R\) is a gr-QF ring if and only if each graded module is a strongly FI-gr-injective module. Suppose that \(R\) is a left gr-coherent ring, then \(l. {\text{FP}}-{\text{gr}}-{\text{dim}} (R)\le 1\) if and only if each FI-gr-injective module is a graded injective module. In addition, it is also proved that \(l.{\text{gr}}-{\text{fiD}} (R) = {\text{sup}}\{{\text{gr}}-{\text{pd}} (L)|L\; {\text{is\; an\; FP-gr-injective\; module}}\}\).