Abstract Graph Convolutional Neural Networks (graph CNNs) have been widely used for graph data representation and semi-supervised learning tasks. However, existing graph CNNs generally use a fifixed graph which may not be optimal for semi-supervised learning tasks. In this paper, we propose a novel Graph Learning-Convolutional Network (GLCN) for graph data representation and semi-supervised learning. The aim of GLCN is to learn an optimal graph structure that best serves graph CNNs for semi-supervised learning by integrating both graph learning and graph convolution in a unifified network architecture. The main advantage is that in GLCN both given labels and the estimated labels are incorporated and thus can provide useful ‘weakly’ supervised information to refifine (or learn) the graph construction and also to facilitate the graph convolution operation for unknown label estimation. Experimental results on seven benchmarks demonstrate that GLCN signifificantly outperforms the state-of-the-art traditional fifixed structure based graph CNNs