A heterogeneous graph is a graph with multiple types of nodes and edges, also known as a heterogeneous information network, which is often used to model systems with rich features and association patterns in the real world. Link prediction between heterogeneous nodes is a fundamental task in network analysis. In recent years, the development of heterogeneous graph neural network (HGNN) has greatly advanced the task of link prediction, which is usually regarded as a feature similarity analysis between nodes or a binary classification problem based on paired node features. However, when learning node feature representations, existing HGNNs usually only focus on the associations between adjacent nodes or the meta-path-based structural information. This not only makes these HGNNs difficult to capture the semantic information of the ring structure inherent in heterogeneous graphs but also ignores the complementarity of structural information at different levels. To solve the above issues, this study proposes a cascade graph convolution network based on multi-level graph structures (CGCN-MGS), which is composed of graph neural networks based on three graph structures of different levels: neighboring, meta-path, and ring structures. CGCN-MGS can mine rich and complementary information from multi-level features and improve the representation ability of the learned node features on the semantics and structure information of nodes. Experimental results on several benchmark datasets show that CGCN-MGS can achieve state-of-the-art performance on the link prediction of heterogeneous graphs.