Abstract: The challenges of building knowledge-grounded retrieval-based chatbots lie in how to ground a conversation on its background knowledge and how to match response candidates with both context and knowledge simultaneously. This paper proposes a method named Filtering before Iteratively REferring (FIRE) for this task. In this method, a context filter and a knowledge filter are first built, which derive knowledge-aware context representations and context-aware knowledge representations respectively by global and bidirectional attention. Besides, the entries irrelevant to the conversation are discarded by the knowledge filter. After that, iteratively referring is performed between context and response representations as well as between knowledge and response representations, in order to collect deep matching features for scoring response candidates. Experimental results show that FIRE outperforms previous methods by margins larger than 2.8% and 4.1% on the PERSONA-CHAT dataset with original and revised personas respectively, and margins larger than 3.1% on the CMU_DoG dataset in terms of top-1 accuracy. We also show that FIRE is more interpretable by visualizing the knowledge grounding process.