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Producing natural and accurate responses like human beings is the ultimate goal of intelligent dialogue agents. So far, most of the past works concentrate on selecting or generating one pertinent and fluent response according to current query and its context. These models work on a one-to-one environment, making one response to one utterance each round. However, in real human-human conversations, human often sequentially sends several short messages for readability instead of a long message in one turn. Thus messages will not end with an explicit ending signal, which is crucial for agents to decide when to reply. So the first step for an intelligent dialogue agent is not replying but deciding if it should reply at the moment. To address this issue, in this paper, we propose a novel Imagine-then-Arbitrate (ITA) neural dialogue model to help the agent decide whether to wait or to make a response directly. Our method has two imaginator modules and an arbitrator module. The two imaginators will learn the agent's and user's speaking style respectively, generate possible utterances as the input of the arbitrator, combining with dialogue history. And the arbitrator decides whether to wait or to make a response to the user directly. To verify the performance and effectiveness of our method, we prepared two dialogue datasets and compared our approach with several popular models. Experimental results show that our model performs well on addressing ending prediction issue and outperforms baseline models.