An important objective in wheat breeding is the development of cultivars with reduced allergenicity and enhanced bread-making quality. In this study, we conducted molecular marker analysis using 1,780 F₁₀ recombinant inbred lines derived from a cross between the hypo-allergenic cultivar Ofree and the Korean bread wheat cultivar Keumgang, and assessed the genotypes associated with ω-5 gliadin, α-gliadin epitopes, bread-making quality, grain hardness, total gliadin content, and the glutenin/gliadin ratio. A Gli-B1 deletion-based ω-5 gliadin-deficient genotype was detected in 18% of the population, whereas no lines lacking Gli-D1-derived ω-5 gliadin or α-gliadin epitopes were identified. The AX-108761918 marker was found to have segregated into TT and GG genotypes at frequencies of 48% and 52%, respectively. Eleven lines carrying favorable combinations of Glu-D1d, Pinb-D1b, and TaIAA10-6D Hap II were selected as promising bread wheat candidates, and a further nine lines combining the Gli-B1 deletion with Glu-D1d and Pinb-D1b were identified as candidates with both reduced-allergenicity and enhanced bread-making quality genotypes. SDS-PAGE analysis confirmed patterns of storage proteins consistent with the results obtained for marker genotyping. These selected lines may provide valuable breeding material for the development hypo-allergenic wheat cultivars with enhanced bread-making quality in Korea.