Virtual assistants aim to build a human-like conversational agent. However, current human-machine conversations still cannot make users feel intelligent enough to build a continued dialog over time. Some responses from agents are usually inconsistent, uninformative, less-engaging and even memoryless. In recent years, most researchers have tried to employ conversation context and external knowledge, e.g. wiki pages and knowledge graphs, into the model which only focuses on solving some special conversation problems in local perspectives. Few researchers are dedicated to the whole capability of the conversational agent which is endowed with abilities of not only passively reacting the conversation but also proactively leading the conversation. In this paper, we first explore the essence of conversations among humans by analyzing real dialog records. We find that some conversations revolve around the same context and topic, and some require additional information or even move on to a new topic. Base on that, we conclude three conversation modes shown in Figure 1 and try to solve how to adapt to them for a continuous conversation. To this end, we define “Adaptive Knowledge-Grounded Conversations” (AKGCs) where the knowledge is to ground the conversation within a multi-turn context by adapting to three modes. To achieve AKGC, a model called MNDB is proposed to Model Natural Dialog Behaviors for multi-turn response selection. To ensure a consistent response, MNDB constructs a multi-turn context flow. Then, to mimic user behaviors of incorporating knowledge in natural conversations, we design a ternary-grounding network along with the context flow. In this network, to gain the ability to adapt to diversified conversation modes, we exploit multi-view semantical relations among response candidates, context and knowledge. Thus, three adaptive matching signals are extracted for final response selection. Evaluation results on two benchmarks indicate that MNDB can significantly outperform state-of-the-art models.