In cloud computing, documents can be outsourced to the cloud server to achieve flexible access control and efficient sharing among multiple users. The outsourced documents can be intelligently searched according to some keywords with the help of cloud server. During the search process, some private information of outsourced documents may be leaked since the keywords may contain sensitive information of users. However, existing privacy-preserving keyword search schemes have high computation complexity, which are not suitable for resource-constrained end devices—that is, the data processing and search trapdoor generation procedures require users to take resource-intensive computations, e.g., high-dimensional matrix operations, exponentiations and bilinear pairings, which are unaffordable by resource-constrained devices. To address the issues of efficiency and privacy for realizing sorted multi-keyword search over outsourced data in clouds, this paper proposes a lightweight privacy-preserving ranked multi-keyword search (PRMS) scheme, which is further extended to allow each outsourced document to be associated with multiple types of keywords. The searched documents can be sorted according to their similarity scores between the search query and the keyword index of documents, so that only when the similarity score exceeds a given threshold, the corresponding searched document will be returned. The security analysis demonstrates that the proposed PRMS schemes can guarantee the privacy of outsourced documents and keywords, and provides unlinkability for search trapdoors. Performance analysis and comparison show the practicality of the proposed PRMS schemes.