Emotional dialogue generation aims to generate appropriate responses that are content relevant with the query and emotion consistent with the given emotion tag. Previous work mainly focuses on incorporating emotion information into the sequence to sequence or conditional variational auto-encoder (CVAE) models, and they usually utilize the given emotion tag as a conditional feature to influence the response generation process. However, emotion tag as a feature cannot well guarantee the emotion consistency between the response and the given emotion tag. In this article, we propose a novel Dual-View CVAE model to explicitly model the content relevance and emotion consistency jointly. These two views gather the emotional information and the content-relevant information from the latent distribution of responses, respectively. We jointly model the dual-view via VAE to get richer and complementary information. Extensive experiments on both English and Chinese emotion dialogue datasets demonstrate the effectiveness of our proposed Dual-View CVAE model, which significantly outperforms the strong baseline models in both aspects of content relevance and emotion consistency.