In the field of multi-style textile defect detection, a common challenge is the difficulty of adapting the inherent detection model to different styles of textile defects. Changes in the color or style of the textile often result in a decrease in the accuracy of defect detection. Relying solely on the model for fine-tuning inspections can lead to catastrophic forgetting, which significantly impacts the performance of the textile defect detector. To address these challenges, a multi-task correlation distillation (MTCD) anomaly detection method based on knowledge distillation and representative sampling is proposed to detect multi-style textile defects. To enable MTCD to detect defects of new-style textiles while maintaining the detection of old-style textiles, two main modules are introduced. The distillation adaptation module (DAM) explores the intra-feature correlation in the feature space of the target detector, allowing the student model to acquire knowledge of new-style textile defect detection while inheriting the teacher model’s detection ability for old-style textile defects. The representative sampling module (RSM) stores representative knowledge of textile defect detection for old-style textiles, facilitating the transfer of knowledge learned from detecting new-style textile defect styles and maintaining the ability to detect defects in old-style textiles. This increases the detection accuracy of the student model for new-style textile defects. The results show that the proposed MTCD method can adapt to the new textile defect detection while maintaining the accuracy of the old textile defect detection and avoiding the problem of catastrophic forgetting. Furthermore, it offers a better balance between stability and plasticity, making it a promising solution for defect detection of multi-style textiles in industrial production environments.