This study explored the quality of hypoallergenic wheat (’O-free’) developed in Korea and optimized the basic ingredients and processing conditions for making ‘O-free’ bread using response surface methodology. Water and yeast amounts and mixing and fermentation times were selected as factors, and each factor’s tested range was set by a central composite design using Design Experts: water 52–60 g, yeast 1.5–4.5 g, mixing time 2.5–5 min, and fermentation time 50–70 min. Bread height, volume, and firmness were analyzed to determine bread quality. Flour quality analysis showed that ‘O-free’ flour’s gluten strength was weak. ‘O-free’ flour exhibited inferior bread-making performance compared to representative bread flour. Water and yeast amounts and mixing time, except for fermentation time, affected bread quality significantly. The interaction between yeast and fermentation also affected bread quality significantly. The optimized condition for making bread using ‘O-free’ flour is 60 g of water, 2.6 g of yeast, 2.5 min of mixing time, and 70.0 min of fermentation time. In conclusion, ‘O-free’ flour with the changed gluten composition showed poor gluten strength and bread-making performance. However, modifying the formulation of the basic ingredients and processing conditions could significantly improve the production of high-quality hypoallergenic bread.