This paper investigates a new task named Conversational Question Generation (CQG) which is to generate a question based on a passage and a conversation history (i.e., previous turns of question-answer pairs). CQG is a crucial task for developing intelligent agents that can drive question-answering style conversations or test user understanding of a given passage. Towards that end, we propose a new approach named Reinforced Dynamic Reasoning network, which is based on the general encoder-decoder framework but incorporates a reasoning procedure in a dynamic manner to better understand what has been asked and what to ask next about the passage into the general encoder-decoder framework. To encourage producing meaningful questions, we leverage a popular question answering (QA) model to provide feedback and fine-tune the question generator using a reinforcement learning mechanism. Empirical results on the recently released CoQA dataset demonstrate the effectiveness of our method in comparison with various baselines and model variants. Moreover, to show the applicability of our method, we also apply it to create multi-turn question-answering conversations for passages in SQuAD.