Traditional multi-label classification algorithms are based on binary label prediction. However， the binary labels can only indicate whether the data has relevant categories， so that they contain less semantic information and cannot fully represent the label semantic information. In order to fully mine the semantic information of label space， a new Multi-Label classification algorithm based on Non-negative matrix factorization and Sparse representation （MLNS） was proposed. In the proposed algorithm， the non-negative matrix factorization and sparse representation technologies were combined to transform the binary labels of data into the real labels， thereby enriching the label semantic information and improving the classification effect. Firstly， the label latent semantic space was obtained by the non-negative matrix factorization of label space， and the label latent semantic space was combined with the original feature space to form a new feature space. Then， the global similarity relation between samples was obtained by the sparse coding of the obtained feature space. Finally， the binary label vectors were reconstructed by using the obtained similarity relation to realize the transformation between binary labels and real labels. The proposed algorithm was compared with the algorithms such as Multi-Label classification Based on Gravitational Model （MLBGM）， Multi-Label Manifold Learning （ML²）， multi-Label learning with label-specific FeaTures （LIFT） and Multi-Label classification based on the Random Walk graph and the K-Nearest Neighbor algorithm （MLRWKNN） on 5 standard multi-label datasets and 5 evaluation metrics. Experimental results show that， the proposed MLNS is better than the compared multi-label classification algorithms in multi-label classification， the proposed MLNS ranks top1 in 50% cases， top 2 in 76% cases and top 3 in all cases.