The rapid deployment of cloud computing provides users with the ability to outsource their data to public cloud for economic savings and flexibility. To protect data privacy, users have to encrypt the data before outsourcing to the cloud, which makes the data utilization, such as data retrieval, a challenging task. It is thus desirable to enable the search service over encrypted cloud data for supporting effective and efficient data retrieval over a large number of data users and documents in the cloud. Existing approaches on encrypted cloud data search either focus on single keyword search or become inefficient when a large amount of documents are present, and thus have little support for the efficient multi-keyword search. In this paper, we propose a light-weight search approach that supports efficient multi-keyword ranked search in cloud computing system. Specifically, we first propose a basic scheme using polynomial function to hide the encrypted keyword and search patterns for efficient multi-keyword ranked search. To enhance the search privacy, we propose a privacy-preserving scheme which utilizes the secure inner product method for protecting the privacy of the searched multi-keywords. We analyze the privacy guarantee of our proposed scheme and conduct extensive experiments based on the real-world dataset. The experiment results demonstrate that our scheme can enable the encrypted multi-keyword ranked search service with high efficiency in cloud computing.