An end-to-end unsupervised domain adaptation method for hyperspectral image (HSI) classification based on graph dual adversarial network is proposed in this paper. First, in order to extract the domain invariant features of the source and target domains, the rich spectral information and spatial position of HSI are used to construct a spectral-spatial nearest neighbor graph, which is input into the graph convolutional network. Then, a prototype adversarial strategy is proposed, which uses the labeled data of source domain to reliably calculate the feature prototypes of different classes. Through the prototype adversarial strategy, the distances between different prototypes are appropriately extended, so that the clusters of different classes are far away from their respective decision boundaries, and the discriminability of features are also enhanced. The dual adversarial strategy is composed of the prototype adversarial strategy and domain adversarial strategy. It is worth noting that the dual adversarial strategy does not require feature extractor and discriminator to work in turn, which can be implemented through a gradient reversal layer. Finally, on the basis of adapting the overall features of both domains via the domain adversarial strategy, the source and target domain features are further adapted by minimizing the correlation alignment loss of each class of samples. Experimental results on two real HSI datasets of Botswana and Kennedy Space Center show the effectiveness of our proposed method.