In this paper, we propose a graph-based kinship reasoning (GKR) network for kinship verification, which aims to effectively perform relational reasoning on the extracted features of an image pair. Unlike most existing methods which mainly focus on how to learn discriminative features, our method considers how to compare and fuse the extracted feature pair to reason about the kin relations. The proposed GKR constructs a star graph called kinship relational graph where each peripheral node represents the information comparison in one feature dimension and the central node is used as a bridge for information communication among peripheral nodes. Then the GKR performs relational reasoning on this graph with recursive message passing. Extensive experimental results on the KinFaceW-I and KinFaceW-II datasets show that the proposed GKR outperforms the state-of-the-art methods.