Multi-label feature selection has been widely used in many domains, such as image classification and disease diagnosis. However, there usually exist missing labels in the label space of data in practice, which destroys the structure and correlation between labels, so that the learning algorithms are difficult to exactly select important features. To address this problem, a Multi-label Feature Selection based on Label-specific feature with Missing Labels (MFSLML) algorithm was proposed. Firstly, the label-specific feature for each class label was obtained via sparse learning method. At the same time, the mapping relations between labels and label-specific features were constructed based on linear regression model, and were used to recover the missing labels. Finally, experiments were performed on 7 datasets with using 4 evaluation metrics. Experimental results show that compared to some state-of-the-art multi-label feature selection algorithms, such as multi-label feature selection algorithm based Max-Dependency and Min-Redundancy (MDMR) and the Multi-label Feature selection with Missing Labels via considering feature interaction (MFML), MFSLML can increase the average precision by 4.61-5.5 percentage points. It can be seen that MFSLML achieves better classification performance.