To build an open-domain multi-turn conversation system is one of the most interesting and challenging tasks in Artificial Intelligence. Many research efforts have been dedicated to building such dialogue systems, yet few shed light on modeling the conversation flow in an ongoing dialogue. Besides, it is common for people to talk about highly relevant aspects during a conversation. And the topics are coherent and drift naturally, which demonstrates the necessity of dialogue flow modeling. To this end, we present the multi-turn cue-words driven conversation system with reinforcement learning method (RLCw), which strives to select an adaptive cue word with the greatest future credit, and therefore improve the quality of generated responses. We introduce a new reward to measure the quality of cue words in terms of effectiveness and relevance. To further optimize the model for long-term conversations, a reinforcement approach is adopted in this paper. Experiments on real-life dataset demonstrate that our model consistently outperforms a set of competitive baselines in terms of simulated turns, diversity and human evaluation.