Incomplete multi-view clustering has become one of the important research problems due to the extensive missing multi-view data in the real world. Although the existing methods have made great progress, there are still some problems: 1) most methods cannot effectively mine the information hidden in the missing data; 2) most methods typically divide representation learning and clustering into two separate stages, but this may affect the clustering performance as the clustering results directly depend on the learned representation. To address these problems, we propose a novel incomplete multi-view clustering method with hierarchical information transfer. Firstly, we design the view-specific Graph Convolutional Networks (GCN) to obtain the representation encoding the graph structure, which is then fused into the consensus representation. Secondly, considering that one layer of GCN transfers one-order neighbor node information, the global graph propagation with the consensus representation is proposed to handle the missing data and learn deep representation. Finally, we design a weight-sharing pseudo-classifier with contrastive learning to obtain an end-to-end framework that combines view-specific representation learning, global graph propagation with hierarchical information transfer, and contrastive clustering for joint optimization. Extensive experiments conducted on several commonly-used datasets demonstrate the effectiveness and superiority of our method in comparison with other state-of-the-art approaches. The code is available at https://github.com/KelvinXuu/GHICMC.