With the significant rise in the demand for infinite storage resource and high-quality retrieval service, cloud computing is deemed to be a highly remarkable technology. For privacy concerns, several research works on ranked multi-keyword search over the encrypted cloud data under multiple data owner model have been developed. However, most of these schemes are vulnerable to keyword guessing attacks and equivalence test attack. Besides, they cannot accurately return the top- $k$ ranked search results from the encrypted data of different data owners to the data users. Obviously, these drawbacks may incur leakage of privacy-sensitive keyword information and the inaccuracy of returned search results. Therefore, in this article, we first propose a novel efficient ranked multi-keyword retrieval scheme with keyword privacy for multiple data owners, which empowers the cloud server to perform multi-keyword search over the cloud data and then, return the top- $k$ ranked search results to data users without leaking any keyword and trapdoor information. Additionally, we show through rigorous security analysis that our scheme is secure against the attacks launched by inside attackers and outside attackers. Finally, the performance evaluation indicates that our scheme has more satisfactory features than the existing ranked multi-keyword search schemes.