This study proposes an optimal design method by applying Prefabricated Buckling Restrained Braces (PF-BRB) to structures with an asymmetrically rigid plan. The results show that considering asymmetric stiffness distribution (Asym) is more effective in reducing dynamic response than a symmetric arrangement (Sym). Notably, at a 20% eccentricity rate, the required reinforcement was minimal. As eccentricity increased, more dampers were concentrated around the eccentric position. Comparing models with 20% and 12% eccentricity, the 20% model exhibited a greater response reduction effect.