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With the advancement of machine learning techniques, data-driven power system dynamic security assessment (DSA) has received great research interests. Traditional methods usually apply one DSA model for one specific fault and cannot simultaneously address different multiple faults by one model. To solve this issue and further improve the DSA accuracy performance, this paper proposes a novel DSA method based on multi-label learning (MLL) with a training database for sufficient and incomplete/uneven coverage labels scenarios. By considering fault correlation between different faults, the proposed MLL-based DSA method can handle multiple faults simultaneously with the high stability assessment accuracy performance. Moreover, this paper provides the detailed optimization process and tight mathematical proof for the proposed MLL-based DSA method. Comprehensive simulation tests and comparisons were conducted on the New England 10-machine 39-bus testing system and the synthetic Illinois 49-machine 200-bus testing system.