The dialogue system that introduces structured knowledge has attracted widespread attention as it can generate more fluent and diverse dialogue replies. However, previous studies only focus on entities in structured knowledge, ignoring the relation between entities and the integrity of knowledge. In this study, a knowledge-aware conversation generation (KCG) model based on the graph convolutional network is proposed. The semantic information of the entity and relation is captured by the knowledge encoder and the representation of the entity is enhanced by the graph convolutional network. Then, the knowledge selection module is applied to obtain the knowledge selection probability distribution of the entities and relations related to the dialogue context. Finally, the knowledge selection probability distribution is fused with the vocabulary probability distribution so that the decoder can select the knowledge or words. In this study, the experiments are conducted on DuConv, a Chinese public data set. The results show that KCG is superior to the current baseline model in terms of automatic evaluation metrics and can generate more fluent and informative replies.