Recently, graph neural networks for semi-supervised classification have been widely studied. However, existing methods only use the information of limited neighbors and do not deal with the inter-class connections in graphs. In this paper, we propose Adaptive aggregation with Class-Attentive Diffusion (AdaCAD), a new aggregation scheme that adaptively aggregates nodes probably of the same class among K-hop neighbors. To this end, we first propose a novel stochastic process, called Class-Attentive Diffusion (CAD), that strengthens attention to intra-class nodes and attenuates attention to inter-class nodes. In contrast to the existing diffusion methods with a transition matrix determined solely by the graph structure, CAD considers both the node features and the graph structure with the design of our class-attentive transition matrix that utilizes a classifier. Then, we further propose an adaptive update scheme that leverages different reflection ratios of the diffusion result for each node depending on the local class-context. As the main advantage, AdaCAD alleviates the problem of undesired mixing of inter-class features caused by discrepancies between node labels and the graph topology. Built on AdaCAD, we construct a simple model called Class-Attentive Diffusion Network (CAD-Net). Extensive experiments on seven benchmark datasets consistently demonstrate the efficacy of the proposed method and our CAD-Net significantly outperforms the state-of-the-art methods. Code is available at https://github.com/ljin0429/CAD-Net.