With the increasing number of mobile applications and the popularity of cloud computing, the combination of these two techniques that named mobile cloud computing (MCC) attracts great attention in recent years. A promising public key encryption scheme, Attribute-Based Encryption (ABE), especially the Ciphertext Policy Attribute-Based Encryption (CP-ABE), has been used for realizing fine-grained access control on encrypted data stored in MCC. However, the computational overhead of encryption and decryption grow with the complexity of the access policy. Thus, maintaining data security as well as efficiency of data processing in MCC are important and challenging issues. In this paper, we propose an efficient encryption method based on CP-ABE, which can lower the overhead on data owners. To further reduce the decryption overhead on data receivers, we additionally propose a verifiable outsourced decryption scheme. By security analysis and performance evaluation, the proposed scheme is proved to be secure as well as efficient.