In this paper, we investigate the problem of facial kinship verification by learning hierarchical reasoning graph networks. Conventional methods usually focus on learning discriminative features for each facial image of a paired sample and neglect how to fuse the obtained two facial image features and reason about the relations between them. To address this, we propose a Star-shaped Reasoning Graph Network (S-RGN). Our S-RGN first constructs a star-shaped graph where each surrounding node encodes the information of comparisons in a feature dimension and the central node is employed as the bridge for the interaction of surrounding nodes. Then we perform relational reasoning on this star graph with iterative message passing. The proposed S-RGN uses only one central node to analyze and process information from all surrounding nodes, which limits its reasoning capacity. We further develop a Hierarchical Reasoning Graph Network (H-RGN) to exploit more powerful and flexible capacity. More specifically, our H-RGN introduces a set of latent reasoning nodes and constructs a hierarchical graph with them. Then bottom-up comparative information abstraction and top-down comprehensive signal propagation are iteratively performed on the hierarchical graph to update the node features. Extensive experimental results on four widely used kinship databases show that the proposed methods achieve very competitive results.