Advancement in cloud computing have revamped the view of modern information technology which is motivating the data owners to outsource their data to the public cloud server like Amazon, Microsoft Azure, Google Drive, etc. With the help of data outsourcing, the organizations can provide reliable data services to their users without any concerns for the data management overhead. One more advantage of outsourcing the data over cloud as SAAS (Storage as a Service) is its cost-effectiveness, scalable and it can be accessed from anywhere and anytime. Considering the large number of data users and documents in cloud, it is crucial for the search service to allow multi-keyword query and provide result similarity ranking to meet the effective data retrieval need. Related works on searchable encryption focus on single keyword search or Boolean keyword search, and rarely differentiate the search results. In this paper, for the first time, we define and solve the challenging problem of privacypreserving multi-keyword ranked search over encrypted cloud data (MRSE), and establish a set of strict privacy requirements for such a secure cloud data utilization system to become a reality. Among various multi-keyword semantics, we choose the efficient principle of "coordinate matching", i.e., as many matches as possible, to capture the similarity between search query and data documents, and further use "inner product similarity" to quantitatively formalize such principle for similarity measurement. We first propose a basic MRSE scheme using secure inner product computation, and then significantly improve it to meet different privacy requirements in two levels of threat models. Thorough analysis investigating privacy and efficiency guarantees of proposed schemes is given, and experiments on the real-world dataset further show proposed schemes indeed introduce low overhead on computation and communication.