In the knowledge-grounded conversation (KGC) task systems aim to produce more informative responses by leveraging external knowledge. KGC includes a vital part, knowledge selection, where conversational agents select the appropriate knowledge to be incorporated in the next response. Mixed initiative is an intrinsic feature of conversations where the user and the system can both take the initiative in suggesting new conversational directions. Knowledge selection can be driven by the user's initiative or by the system's initiative. For the former, the system usually selects knowledge according to the current user utterance that contains new topics or questions posed by the user; for the latter, the system usually selects knowledge according to the previously selected knowledge. No previous study has considered the mixed-initiative characteristics of knowledge selection to improve its performance.In this paper, we propose a mixed-initiative knowledge selection method (MIKe) for KGC, which explicitly distinguishes between user-initiative and system-initiative knowledge selection. Specifically, we introduce two knowledge selectors to model both of them separately, and design a novel initiative discriminator to discriminate the initiative type of knowledge selection at each conversational turn. A challenge for training MIKe is that we usually have no labels for indicating initiative. To tackle this challenge, we devise an initiative-aware self-supervised learning scheme that helps MIKe to learn to discriminate the initiative type via a self-supervised task. Experimental results on two datasets show that MIKe significantly outperforms state-of-the-art methods in terms of both automatic and human evaluations, indicating that it can select more appropriate knowledge and generate more informative and engaging responses.