Attribute-based searchable encryption (ABSE) schemes provide searchability and fine-grained access control over encrypted data in the cloud. Although prior ABSE schemes are designed to provide data protection and retrieval efficiency, they are suffering from the following issues. 1) A key-escrow problem, which may lead to the misuse of the user’s secret key. 2) A single keyword search, which may produce irrelevant search results and also vulnerable in real-world applications. 3) A static policy update mechanism, which incurs high computation and communication overheads. In this paper, we propose a novel ABSE scheme called a key-escrow free attribute-based multi-keyword search with dynamic policy updates in cloud computing (KAMS-PU) to addresses all the above-stated issues. The security analysis proves that KAMS-PU is secure against malicious authority attacks and chosen keyword attack (CKA) in the random oracle model. Furthermore, performance analysis proves that KAMS-PU is efficient and practical in real-world applications.