Abstract Though great progress has been made for human-machine conversation, current dialogue system is still in its infancy: it usually converses passively and utters words more as a matter of response, rather than on its own initiatives. In this paper, we take a radical step towards building a human-like conversational agent: endowing it with the ability of proactively leading the conversation (introducing a new topic or maintaining the current topic). To facilitate the development of such conversation systems, we create a new dataset named DuConv where one acts as a conversation leader and the other acts as the follower. The leader is provided with a knowledge graph and asked to sequentially change the discussion topics, following the given conversation goal, and meanwhile keep the dialogue as natural and engaging as possible. DuConv enables a very challenging task as the model needs to both understand dialogue and plan over the given knowledge graph. We establish baseline results on this dataset (about 270K utterances and 30k dialogues) using several state-of-the-art models. Experimental results show that dialogue models that plan over the knowledge graph can make full use of related knowledge to generate more diverse multi-turn conversations. The baseline systems along with the dataset are publicly available