Generating emotional responses is crucial for building human-like dialogue systems. However, existing studies have focused only on generating responses by controlling the agents' emotions, while the feelings of the users, which are the ultimate concern of a dialogue system, have been neglected. In this paper, we propose a novel variational model named EmoElicitor to generate appropriate responses that can elicit user's specific emotion. We incorporate the next-round utterance after the response into the posterior network to enrich the context, and we decompose single latent variable into several sequential ones to guide response generation with the help of a pre-trained language model. Extensive experiments conducted on real-world dataset show that EmoElicitor not only performs better than the baselines in term of diversity and semantic similarity, but also can elicit emotion with higher accuracy.