Recently deep learning has been used in Medical subject headings (MeSH) indexing to reduce the time and monetary cost by manual annotation, including DeepMeSH, TextCNN, etc. However, these models still suffer from failing to capture the complex correlations between MeSH terms. To this end, we introduce Graph Convolution Network (GCN) to learn the relationship between these terms, and present a novel Hybrid Graph Convolution Net for MeSH index (HGCN4MeSH). Basically, we utilize two BiGRUs to learn the embedding representation of the abstract and the title of the MeSH index text respectively. At the same time, we establish the adjacency matrix of MeSH terms based on the co-occurrence relationships in Corpus, which is easy to apply for GCN representation learning. On the basis of learning the mixed representation, the prediction problem of the MeSH index keywords is transformed into an extreme multi-label classification problem after the attention layer operation. Experimental results on two datasets show that HGCN4MeSH is competitive compared with the state-of-the-art methods.