To integrate the label structures, which describe semantic correlations among labels, into the learned common representations, many existing methods leverage the label embeddings learned according to label structures, to map the data of different modalities into a common representation space. However, these methods cannot fully discover the semantic correlation between labels. In this paper, we propose an Adaptive Multi-label Structure Preserving Network (AMLSPN) to dynamically learn the multi-label correlations and multi-label embeddings for learning common representations, which can preserve the label structures. Our method introduces a series of multi-label correlation matrices to capture the structures of multi-label nodes in the multi-label graph. Moreover, we present a novel hierarchical correlation loss to supervise the learning process of these multi-label correlation matrices. Additionally, we introduce a group GCN to enhance the training speed of our model. Extensive evaluations on three benchmark datasets demonstrate that our proposed AMLSPN outperforms the state-of-the-art methods.