Since cloud computing has been playing an increasingly important role in real life, the privacy protection in many fields has been paid more and more attention, especially, in the field of Personal Health Record (PHR). The traditional ciphertext-policy attribute based encryption(CP-ABE) provides the fine-grained access control policy for encrypted PHR data, but the access policy is also sent along with ciphertext explicitly. However, the access policy will reveal the users’ privacy because it contains too much sensitive information of the legitimate data users. Hence it is important to protect users’ privacy by hiding access policies. In most of the previous schemes, although the access policy is hidden, they face two practical problems: (1) these schemes do not support large attribute universe, so their practicality in PHR is greatly limited, and (2) the cost of decryption is especially high since the access policy is embedded in ciphertext. To address these problems, we construct a CP-ABE scheme with efficient decryption, where both the size of public parameters and the cost of decryption are constant. Moreover, we also show the proposed scheme achieves full security in the standard model under static assumptions by using the dual system encryption method.