Protecting private data becomes very important in communication with the widespread adoption of the cloud storage system; for example, Dropbox, SkyDrive and iCloud. A user should be able to access his private data from cloud, and efficiently retrieves data which he wants. In fact, a straightforward solution to protecting user's private data is encryption. Relying on keyword search over the encrypted data is very useful and efficient to retrieve from the untrusted cloud storage. In this scenario, a sender can send encrypted data, and the receiver can generate trapdoors from keywords to retrieve those data which include the keywords. Recently, Zhang and Zhang proposed a field-free public key encryption with user-friendly keywords search. In this paper, we present a searchable public key encryption with user-friendly keywords search. The proposed scheme is secure based on secret sharing and the hardness of discrete logarithm problem. It is more efficient than Zhang and Zhang's scheme on computation. Moreover, we also analyze that this scheme satisfies some properties, which is suitable to data deliver/retrieval in cloud storage.