Genetic Diversity of HMW-GS and the Correlation of Grain Quality Traits in Bread Wheat (Triticum aestivum L.) in Hubei Province, China

High-molecular-weight glutenin subunits (HMW-GS) are an important component of total cereal proteins in wheat. It is closely related to the processing quality of flour. Here, we analyzed allelic variations at the Glu-1 locus in 163 wheat accessions from Hubei Province, China with SDS-PAGE. Among the 15 alleles detected, alleles 1, 7+8, and 2+12 were the major alleles, and 7, 6+8, and 2+10 were rare alleles. The breeding lines had higher genetic diversity than the commercial varieties. Alleles 7 and 6+8 significantly reduced the grain protein content and wet gluten content of wheat. The “1, 7+9, 5+10” and “1, 14+15, and 2+12” allelic combinations significantly increased the grain protein content, hardness index, test weight, and wet gluten content of wheat. Alleles 7+9, 14+15, and 5+10 were identified as alleles related to high wheat quality. The “1, 7, 5+10”, “1, 6+8, 5+10”, “null, 7+9, 2+12”, “1, 14+15, 2+12”, and “1, 7+9, 5+10” allelic combinations had greater effects on wheat grain quality traits. These results demonstrate the effects of HMW-GS on wheat grain quality traits and provide a reference for the genetic improvement of wheat quality.