Feature extraction is one of the most important tasks in multi-label learning. The performance of multi-label classification can be effectively improved by reducing the dimension of multi-label datasets. Although research on multi-label feature extraction has received extensive attention and made significant progress, further improvement is still necessary. One of the concerns is robustness, where existing multi-label feature extraction algorithms are usually sensitive to noise and outliers. To address this issue, a robust multi-label relief feature selection algorithm based on fuzzy margin co-optimization, called ML-FS-FM, is proposed in this article. Under the multi-label learning framework, the classical fuzzy relief feature weighting algorithm is introduced to ML-FS-FM, which involves the mechanisms of fuzzy feature weighting, fuzzy nearest neighbor and fuzzy instance force coefficient, so as to effectively reduce the influence of noise and outliers, and to extract feature subsets that are beneficial to the classification task. The effectiveness of the proposed algorithm is verified by a large number of experiments on multi-label datasets.