To address the problem that most existing searchable encryption schemes do not support Boolean search for multiple keywords and cannot satisfy the forward security of indexes, a Boolean searchable encryption scheme supporting forward security (BSFS) is proposed in this paper. Two problems are solved by using techniques related to set theory and cryptographic knowledge: (1) The ability to implement Boolean search for multiple keywords based on traditional searchable encryption schemes; (2) The forward security of the index is satisfied by the clever construction of the index. The security analysis shows that the correctness, confidentiality and forward security of the scheme are guaranteed and that it has a high degree of practical applicability.