The quality of wheat primarily depends on its storage protein quality, especially in regards to gluten content and high-molecular-weight glutenin subunits (HMW-GS). The number of HMW-GS alleles is limited in bread wheat (Triticum aestivum L.), whereas it is abundant in wheat relatives. Therefore, HMW-GS alleles from wheat relatives could provide a potential for improving quality in wheat breeding. Thinopyrum elongatum (EE) is one of the relatives of wheat. The E genome is closely related to the ABD genome in wheat; therefore, Th. elongatum is often used as an excellent exogenous gene donor for wheat genetic improvement. In this study, the high-molecular glutenin subunit gene was cloned and sequenced from Th. elongatum. A specific molecular marker for identifying the Glu-1Ey subunit gene was developed and applied to detected wheat-Th. elongatum alien introgression lines. Quality analysis indicated that the substitution and addition lines containing Th. elongatum alleles significantly (p < 0.05) increased grain protein content by 3.76% to 5.11%, wet-gluten content by 6.55% to 8.73%, flour 8-MW by 0.25% to 6.35%, and bread volume value by 33.77 mL to 246.50 mL, in comparing it with Chinese Spring. The GMP content and lactic acid SRC showed significant positive correlations with flour processing quality and might be used as indicators for wheat quality. The results were expected to provide a novel route for improving processing quality in wheat quality breeding.