We propose Aggregation with Class-Attentive Diffusion (AggCAD), a novel aggregation scheme for semi-supervised classification on graphs, which enables the model to embed more favorable node representations for better class separation. To this end, we propose a novel Class-Attentive Diffusion (CAD) which 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 the class-attentive transition matrix which utilizes the classifier. In addition, we further propose an adaptive scheme for AggCAD that leverages different reflection ratios of the diffusion result for each node depending on the local class-context. As the main advantage, AggCAD alleviates the problem of undesired mixing of inter-class features caused by discrepancies between node labels and the graph structure. Built on AggCAD, we construct Class-Attentive Diffusion Network for semi-supervised classification. Comprehensive experiments demonstrate the validity of AggCAD and the results show that the proposed method significantly outperforms the state-of-the-art methods on three benchmark datasets.