Recently, deep neural networks (DNNs) have been widely used in hyperspectral image change detection (HSI-CD). Generally, training such a DNN-based HSI-CD network often requires a large number of labeled training samples. However, it is time-consuming, labor-intensive, or even infeasible to label training samples in practice. In this article, we propose a feature mutual representation-based graph domain adaptive network (FGDANet) for unsupervised HSI-CD. This method constructs a pseudosiamese backbone consisting of two customized unsupervised learning domains, which can make full use of the information from different domains through the graph domain adaptation strategy to improve the feature expression capability and generalization. There are three key characteristics: first, in each customized unsupervised learning domain, a graph convolutional network (GCN)-based difference feature extraction architecture is designed to model the local and global dependence among the features of multitemporal HSIs; second, a progressive graph-to-pixel joint constraint strategy (PJCS) is proposed to provide the high-confidence training sample labels for the unsupervised learning of the network in each domain; and third, the homogeneous mutual representation joint graph feature alignment (HJGFA) module of the graph domain adaptation strategy can make full use of the difference features from the two domains through the information interaction to facilitate the model to capture the changed and unchanged essential characteristics. The experimental results on four HSI datasets demonstrate the superiority of the proposed FGDANet. Code is available at https://github.com/Jiahuiqu/FGDANet.