In data mining and machine learning applications, the cost of collecting the features have to be taken into account in the feature selection. The cost-sensitive feature selection is widely discussed in single-label. However, there is little theoretical analysis on the issue of cost-sensitive multi-label feature selection. In coping with this problem, we propose a novel cost-sensitive multi-label feature selection based on positive approximation. In this proposed model, the feature significance is redefined by combination of the positive approximation and the feature cost on the basis of feature cores. Theoretical analysis and experimental results demonstrate the effectiveness and efficiency of the proposed algorithm thoroughly performed on three real multi-label datasets.