Conversational recommender system (CRS) interacts with users through multi-turn dialogues in natural language, which aims to provide high-quality recommendations for user's instant information need. Although great efforts have been made to develop effective CRS, most of them still focus on the contextual information from the current dialogue, usually suffering from the data scarcity issue. Therefore, we consider leveraging historical dialogue data to enrich the limited contexts of the current dialogue session. In this paper, we propose a novel multi-grained hypergraph interest modeling approach to capture user interest beneath intricate historical data from different perspectives. As the core idea, we employ hypergraph to represent complicated semantic relations underlying historical dialogues. In our approach, we first employ the hypergraph structure to model users' historical dialogue sessions and form a session-based hypergraph, which captures coarse-grained, session-level relations. Second, to alleviate the issue of data scarcity, we use an external knowledge graph and construct a knowledge-based hypergraph considering fine-grained, entity-level semantics. We further conduct multi-grained hypergraph convolution on the two kinds of hypergraphs, and utilize the enhanced representations to develop interest-aware CRS. Extensive experiments on two benchmarks ReDial and TG-ReDial validate the effectiveness of our approach on both recommendation and conversation tasks. Code is available at: https://github.com/RUCAIBox/MHIM.

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