Information diffusion prediction is an important task which attempts to predict the potential users that will be affected in an information cascade. Existing studies utilize the user interactions in the diffusion graphs with past diffusion records and user relationships in social networks, and capture the structural proximity of those networks to model user similarities for diffusion prediction. However, they ignore structural similarity of the networks, namely user roles, which is of great significance. Actually, a user's future reposting behavior depends on the roles of previous participants. For instance, sometimes people may not respond to discussions of their so-so friends until a more influential friend joins in. Also, user roles change over time. In this paper, we propose a novel Role-based Dynamic Graph Convolutional Network (RD-GCN) which captures the dependencies of dynamic user roles and information diffusion, and jointly learns the two parts. Specifically, the original diffusion graph is divided into subgraphs according to timestamps and users' preferences and roles are captured from those sequential subgraphs and social networks. Also, gated mechanisms are introduced to incorporate users' different tendencies to be influenced by roles. The experiments on three public datasets demonstrate that RD-GCN significantly outperforms state-of-the-art models, verifying the effectiveness of our proposed model.