Information explosion is a common problem in the information age. In order that valuable information can be extracted rapidly from massive text data, automatic summarization technologies have become a research priority in the field of natural language processing (NLP). The purpose of multi-document summarization is to refine important content from a group of documents on the same topic and thereby help users get key information quickly. To address the problems of incomplete information and high redundancy in multi-document summarizations, this study proposes an extractive summarization method based on multi-granularity semantic interaction that combines the multi-granularity semantic interaction network with maximal marginal relevance (MMR). Semantic interaction with different granularities is used to train sentence representation and key information with different granularities is captured to ensure the comprehensiveness of the summarization. In addition, modified MMR is employed to ensure the low redundancy of the summarization. The sentences in the input documents are scored by learning to rank, and summary sentences are then extracted. Experimental results on the Multi-News dataset show that the proposed extractive multi-document summarization model based on multi-granularity semantic interaction outperforms some baseline models such as LexRank and TextRank.