Abstract: Focusing on the problem of confidentiality and availability of user data in cloud storage environment, we study the encrypted search method with multi-keyword. Aiming at the practical demand, we propose a multi-keyword encrypted search scheme with relevance ranking (MES-RR) in dual-server model, which can not only achieve secure multi-keyword encrypted search, but also ensure efficient search result sorting. We construct a relevance-based keyword index with the tools of TF-IDF weighting scheme and Paillier homomorphic cryptosystems, which not only obtains optimize computational complexity but also reduces storage complexity. We design a dual-server model architecture to perform the collaborated mechanism. Based on that, we design a secure sorting protocol between the two collaborated servers to sort the encrypted search results, which outputs private ranking result to user. In terms of security, we design the security model of MES-RR under honest but curious threat scenario, and give formal security analysis. The result shows that MES-RR can resist adaptive chosen keyword attacks under the random oracle model (IND-CKA2). The performance analysis shows that compared with the previous multi-keyword encrypted search scheme that supports result sorting, MES-RR reduces the storage cost and interactions, and is applicable to the cloud storage environment in the real world.