In this paper, we are concerned with Tate homology tor̂ $\widehat {\text {tor}}$of modules of finite Gorenstein FI-flat dimension. We determine connections between Tate, relative and absolute homology. Furthermore, we discuss Tate homology tor̂ $\widehat {\text {tor}}$of a FI-cotorsion modules of finite Gorenstein FI-flat dimension over right coherent rings.