Abstract: In this paper, we propose a Chinese multi-turn topic-driven conversation dataset, NaturalConv, which allows the participants to chat anything they want as long as any element from the topic is mentioned and the topic shift is smooth. Our corpus contains 19.9K conversations from six domains, and 400K utterances with an average turn number of 20.1. These conversations contain in-depth discussions on related topics or widely natural transition between multiple topics. We believe either way is normal for human conversation. To facilitate the research on this corpus, we provide results of several benchmark models. Comparative results show that for this dataset, our current models are not able to provide significant improvement by introducing background knowledge/topic. Therefore, the proposed dataset should be a good benchmark for further research to evaluate the validity and naturalness of multi-turn conversation systems. Our dataset is available at https://ai.tencent.com/ailab/nlp/dialogue/#datasets.