Knowledge graph (KG) embedding models map nodes and edges to fixed-length vectors and obtain the similarity of nodes as the output of a scoring function to predict missing links between nodes. KG embedding methods based on graph convolutional networks (GCNs) have recently gained significant attention due to their ability to add information of neighboring nodes into the nodes’ embeddings. However, existing GCNs are primarily based on real-valued embeddings, which have high distortion, particularly when modeling graphs with varying geometric structures. In this paper, we propose complex graph convolutional network (ComplexGCN), a novel extension of the standard GCNs in complex space to combine the expressiveness of complex geometry with GCNs for improving the representation quality of KG components. The proposed ComplexGCN comprises a set of complex graph convolutional layers and a complex scoring function based on PARATUCK2 decomposition: the former includes information of neighboring nodes into the nodes’ embeddings, while the latter leverages these embeddings to predict new links between nodes. The proposed model demonstrates enhanced performance compared to existing methods on the two recent standard link prediction datasets. •Real embeddings usually suffer from high distortion.•An extension of graph convolution network is introduced with complex embeddings.•A novel complex scoring function based on PARATUCK2 decomposition is introduced.•The results show that complex embeddings lead to performance improvement.