Over the past few years making use of deep networks, including convolutional neural networks (CNNs) and recurrent neural networks (RNNs), classifying hyperspectral images has progressed significantly and gained increasing attention. In spite of being successful, these networks need an adequate supply of labeled training instances for supervised learning, which, however, is quite costly to collect. On the other hand, unlabeled data can be accessed in almost arbitrary amounts. Hence it would be conceptually of great interest to explore networks that are able to exploit labeled and unlabeled data simultaneously for hyperspectral image classification. In this article, we propose a novel graph-based semisupervised network called nonlocal graph convolutional network (nonlocal GCN). Unlike existing CNNs and RNNs that receive pixels or patches of a hyperspectral image as inputs, this network takes the whole image (including both labeled and unlabeled data) in. More specifically, a nonlocal graph is first calculated. Given this graph representation, a couple of graph convolutional layers are used to extract features. Finally, the semisupervised learning of the network is done by using a cross-entropy error over all labeled instances. Note that the nonlocal GCN is end-to-end trainable. We demonstrate in extensive experiments that compared with state-of-the-art spectral classifiers and spectral-spatial classification networks, the nonlocal GCN is able to offer competitive results and high-quality classification maps (with fine boundaries and without noisy scattered points of misclassification).