The traditional wheat 1B/1R translocation lines usually have poor processing quality and are not suitable for processing strong gluten foods. In order to improve the processing quality of wheat 1B/1R translocation lines, a cross was made between a wheat 1B/1R translocation line variety Kenong 199 with the high molecular weight glutenin subunits (HMW-GSs) composition of 1/7+9/2+12 and a strong gluten spring wheat variety Jinqiang 6 with the HMW-GSs composition of 1/7OE+8*/5+10. From an F4 generation line, we used molecular markers to screen out some plants in which the Bx7OE gene and the secalin genes were recombined on the same chromosome and other types of plants with no recombination between the two loci. The results of SSR assay indicated that the recombination occurred on the long arm of 1B chromosome. Some plants with difference in Glu-B1 locus and their parents were selected for SIG determination, the results showed that compared with the parent Kenong 199, the SIG values of the 1B/1R translocation lines pyramiding 5+10 high-quality subunits were significantly increased, but their SIG values were still significantly lower than that of the strong gluten parent Jinqiang 6. When 5+10 and Bx7OE high-quality subunits were simultaneously pyramided into the 1B/1R translocation lines, the SIG values of some plants increased further and reached the level of the strong gluten parent Jinqiang 6, indicating the quality defects of these 1B/1R translocation lines were completely compensated. This study provides a new idea for breeding strong gluten wheat 1B/1R translocation lines.