Dialog topic management and background knowledge selection are essential factors for the success of knowledge-grounded open-domain conversations. However, existing models are primarily performed with symmetric knowledge bases or stylized with pre-defined roles between conversational partners, while people usually have their own knowledge before a real chit-chat. To address this problem, we propose a dynamic knowledge graph-based topical conversation model (DKGT). Given a dialog history context, our model first builds knowledge graphs from the context as an imitation of human’s ability to form logical relationships between known and unknown topics during a conversation. This logical information will be fed into a topic predictor to promote topic management, then facilitate background knowledge selection and response generation. To the best of our knowledge, this is the first attempt to dynamically form knowledge graphs between chatting topics to assist dialog topic management during a conversation. Experimental results manifest that our model can properly schedule conversational topics and pick suitable knowledge to generate informative responses comparing to several strong baselines.