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In multi-label learning, the issue of missing labels brings a major challenge. Many methods attempt to recovery missing labels by exploiting low-rank structure of label matrix. However, these methods just utilize global low-rank label structure, ignore both local low-rank label structures and label discriminant information to some extent, leaving room for further performance improvement. In this paper, we develop a simple yet effective discriminant multi-label learning (DM2L) method for multi-label learning with missing labels. Specifically, we impose the low-rank structures on all the predictions of instances from the same labels (local shrinking of rank), and a maximally separated structure (high-rank structure) on the predictions of instances from different labels (global expanding of rank). In this way, these imposed low-rank structures can help modeling both local and global low-rank label structures, while the imposed high-rank structure can help providing more underlying discriminability. Our subsequent theoretical analysis also supports these intuitions. In addition, we provide a nonlinear extension via using kernel trick to enhance DM2L and establish a concave-convex objective to learn these models. Compared to the other methods, our method involves the fewest assumptions and only one hyper-parameter. Even so, extensive experiments show that our method still outperforms the state-of-the-art methods.