Supervised multi-class learning arises in many application domains such as biology, computer vision, social network analysis, and information retrieval. These applications often involve high-dimensional data, which not only significantly increase the time and space requirement of the underlying algorithms but also degrade their performance due to the curse of dimensionality. Feature selection has been proven effective and efficient for preparing high-dimensional data for many learning tasks. Traditional feature selection algorithms for multi-class data assume the independence of label categories and select features with the capability to distinguish samples from different classes. However, class labels in multi-class data may be correlated and little work exists for exploiting label correlation in multi-class feature selection. In this paper, we investigate label correlation in feature selection for multi-class data. In particular, we provide a principled approach for capturing label correlation and propose an Embedded Supervised Feature Selection (ESFS) framework, which embeds label correlation modeling in supervised feature selection for multi-class data. Experiments on both synthetic data and various types of public benchmark datasets show that the proposed framework effectively captures the multi-class label correlation and significantly outperforms existing state-of-the-art baseline methods.