Contextual bandit algorithms provide principled online learning solutions to balance the exploitation-exploration trade-off in various applications such as recommender systems. However, the learning speed of the traditional contextual bandit algorithms is often slow due to the need for extensive exploration. This poses a critical issue in applications like recommender systems, since users may need to provide feedbacks on a lot of uninterested items. To accelerate the learning speed, we generalize contextual bandit to conversational contextual bandit. Conversational contextual bandit leverages not only behavioral feedbacks on arms (e.g., articles in news recommendation), but also occasional conversational feedbacks on key-terms from the user. Here, a key-term can relate to a subset of arms, for example, a category of articles in news recommendation. We then design the Conversational UCB algorithm (ConUCB) to address two challenges in conversational contextual bandit: (1) which key-terms to select to conduct conversation, (2) how to leverage conversational feedbacks to accelerate the speed of bandit learning. We theoretically prove that ConUCB can achieve a smaller regret upper bound than the traditional contextual bandit algorithm LinUCB, which implies a faster learning speed. Experiments on synthetic data, as well as real datasets from Yelp and Toutiao, demonstrate the efficacy of the ConUCB algorithm.