Neural generative models have become popular and achieved promising performance on short-text conversation tasks. They are generally trained to build a 1-to-1 mapping from the input post to its output response. However, a given post is often associated with multiple replies simultaneously in real applications. Previous research on this task mainly focuses on improving the relevance and informativeness of the top one generated response for each post. Very few works study generating multiple accurate and diverse responses for the same post. In this paper, we propose a novel response generation model, which considers a set of responses jointly and generates multiple diverse responses simultaneously. A reinforcement learning algorithm is designed to solve our model. Experiments on two short-text conversation tasks validate that the multiple responses generated by our model obtain higher quality and larger diversity compared with various state-ofthe-art generative models.