Recently, graph convolutional networks (GCNs) and their variants have achieved remarkable successes for the graph-based semisupervised node classification problem. With a GCN, node features are locally smoothed based on the information aggregated from their neighborhoods defined by the graph topology. In most of the existing methods, the graph typologies only contain positive links which are deemed as descriptions for the feature similarity of connected nodes. In this article, we develop a novel GCN-based learning framework that improves the node representation inference capability by including negative links in a graph. Negative links in our method define the inverse correlations for the nodes connected by them and are adaptively generated through a neural-network-based generation model. To make the generated negative links beneficial for the classification performance, this negative link generation model is jointly optimized with the GCN used for class inference through our designed training algorithm. Experiment results show that the proposed learning framework achieves better or matched performance compared to the current state-of-the-art methods on several standard benchmark datasets.