In textile manufacturing, the presence of fabric flaws is inevitable. However, traditional nesting methods often overlook these flaws, leading to compromised product quality or delivery delays due to the need for extra fabric. This research addresses the two-dimensional irregular nesting problem for flawed fabric by innovatively proposing the Flaw-Avoidance Irregular Nesting Algorithm (FAINA). Initially, flaws on the textile fabric are conceptualized as specially prioritized pieces, with an appropriate genetic algorithm utilized to generate the sequence for arranging regular pieces. Subsequently, the strategy for generating No-Fit-Polygon is refined to achieve flaw circumvention and ascertain the pieces’ adjacency positioning. Finally, an integrated sorting scheme for flaw-free pieces is obtained by calculating the tailored fitness based on the adjacency positioning relationship and flaw information, optimizing the arrangement of irregular pieces to enhance fabric utilization. Our algorithm guarantees avoidance of flaws of any shape, number and size while optimizing the layout to improve material usage. It is tested on datasets with 10, 30, 50 and 314 pieces on flawed fabric and compared to random, greedy, genetic algorithms that ignore flaws. The results demonstrate a 2% to 13% improvement in area utilization by the proposed algorithm, ensuring all pieces are uncontaminated. Our research offers significant technical support for material utilization and cost control in production, showcasing substantial practical value.