High molecular weight glutenin subunits (HMW-GSs) are important seed storage proteins in wheat (Triticum aestivum) that determine wheat dough elasticity and processing quality. Clarification of the defined effectiveness of HMW-GSs is very important to breeding efforts aimed at improving wheat quality. To date, there have no report on the expression silencing and quality effects of 1Bx20 and 1By20 at the Glu-B1 locus in wheat. A wheat somatic variation line, AS208, in which both 1Bx20 and 1By20 at Glu-B1 locus were silenced, was developed recently in our laboratory. Evaluation of agronomic traits and seed storage proteins by sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) and reversed-phase high performance liquid chromatography (RP-HPLC) indicated that AS208 was highly similar to its parental cultivar Lunxuan987 (LX987), with the exception that the composition and expression of HMW-GSs was altered. The 1Bx20 and 1By20 in AS208 were further identified to be missing by polymerase chain reaction (PCR) and quantitative real-time RT-PCR (qRT-PCR) assays. Based on the PCR results for HMW-GS genes and their promoters in AS208 compared with LX987, 1Bx20 and 1By20 were speculated to be deleted in AS208 during in vitro culture. Quality analysis of this line with Mixograph, Farinograph, and Extensograph instruments, as well as analysis of bread-making quality traits, demonstrated that the lack of the genes encoding 1Bx20 and 1By20 caused various negative effects on dough processing and bread-making quality traits, including falling number, dough stability time, mixing tolerance index, crude protein values, wet gluten content, bread size, and internal cell structure. AS208 can potentially be used in the functional dissection of other HMW-GSs as a plant material with desirable genetic background, and in biscuit making industry as a high-quality weak gluten wheat source.