Abstract Recently, graph representation learning based on autoencoders has received much attention. However, these methods suffer from two limitations. First, most graph autoencoders ignore the reconstruction of either the graph structure or the node attributes, which often leads to a poor latent representation of the graph-structured data. Second, for existing graph autoencoders models, the encoder and decoder are mainly composed of an initial graph convolutional network (GCN) or its variants. These traditional GCN-based graph autoencoders more or less encounter the problem of incomplete filtering, which causes these models to be unstable in practical applications. To address the above issues, this paper proposes the Graph convolutional Autoencoders with co-learning of graph Structure and Node attributes (GASN) based on variational autoencoders. Specifically, the proposed GASN encodes and decodes the node attributes and graph structure comprehensively in the graph-structured data. Furthermore, we design a completely low-pass graph encoder and a high-pass graph decoder. The experimental results on real-world datasets demonstrate that the proposed GASN achieves state-of-the-art performance on node clustering, link prediction, and visualization tasks.