Generating diverse and consistent responses is the ultimate goal of a persona-based dialogue. Although many studies have been conducted, the generated responses tend to be generic and bland due to the personas’ limited descriptiveness. Therefore, it is necessary to expand the given personas for more attractive responses. However, indiscriminate expansion of personas threaten the consistency of responses and therefore reduce the interlocutor’s interest in conversation. To alleviate this issue, we propose a consistent persona expansion framework that improves not only the diversity but also the consistency of persona-based responses. To do so, we define consistency criteria to avoid possible contradictions among personas as follows: 1) Intra-Consistency and 2) Inter-Consistency. Then, we construct a silver profile dataset to deliver the ability to conform with the consistency criteria to the expansion model. Finally, we propose a persona expansion model with an encoder-decoder structure, which considers the relatedness and consistency among personas. Our experiments on the Persona-Chat dataset demonstrate the superiority of the proposed framework.