Abstract: Let W be a class of modules that contained all injective modules. By introducing the cover W-Gorenstein flat dimension of modules over associativering, we described that a class of  W-Gorenstein flat modules was projectively resolving, and proved that for every Rmodule M and every positiveinteger n, if the cover 〖WTHT〗W〖WT〗Gorenstein flat dimension of Rmodule M was n, then there existed an exact sequence of Rmodules 0→K→H→M→0 such that fd(K)=n-1 and H was W-Gorenstein flat module. At the same time, we proved that the W-Gorenstein flat dimension was less than the cover W-Gorenstein flat dimension and they were equivalent when the cover W-Gorenstein flat dimension was finite.

Key words: W-Gorenstein flat dimension, W-GF closed ring, cover W-Gorenstein flat dimension