GCN-based clustering schemes cannot interactively fuse feature information of nodes and topological structure information of graphs, leading to insufficient accuracy of clustering results. Moreover, the deep clustering model based on graph structure is vulnerable to the attack of adversarial samples leading to the reduced robustness of the model. To solve the above two problems, this paper proposes a robust clustering model based on attention mechanism and graph convolutional network (GCN), named AG-cluster. This model firstly uses graph attention network and GCN to learn the feature information of nodes and the topological structure information of graphs, respectively. Then the representation results of the above two learning modules are interactively fused by the interlayer transfer operator. Finally, the model is trained end-to-end using a self-supervised training module to optimize the clustering results of the model. In particular, an efficient graph purification defense mechanism (GPDM) is designed to resist adversarial attacks on graph data to improve the robustness of the model. Experimental results show that AG-cluster outperforms the other four benchmark methods, specifically, AG-cluster improves 7.6% in Accuracy and 11.5% in NMI compared to the best benchmark method. Besides, the new model still shows higher robustness and stronger transferability under multiple attacks.