In view of the searchable encryption technology in cloud storage services, this paper solves the following three problems：Firstly, most of the traditional searchable encryption methods only support single keyword search, and when the security index is too large, the search time cost is too high; Secondly, most of the existing schemes use inverted index for quick search, but inverted index does not support dynamic keyword update; Thirdly, most of the existing schemes can’t sort the search files efficiently according to the importance of keywords for some on-demand users. In this paper, a top-k boolean searchable encryption scheme based on multiple keywords (TBSE) is proposed. In the scheme, Goldwasser-Micalli and 2DNF encryption algorithms are used to construct a secure, index supporting dynamic update. Based on the set theory and boolean search, keyword intersection index and intersection search token are constructed to realize boolean search for multiple keywords. The top-k sorting is realized by fractional index constructed by using TF-IDF weighting technology and security coprocessor. The security analysis shows that the scheme can fully guarantee the security of the given ciphertext model and the known background model. The experiments prove that the scheme improves the efficiency of multi keywords Boolean search and index storage.