In an anonymous ciphertext-policy attribute-based encryption (CP-ABE) scheme, the encryptor-specified access structure is hidden in ciphertexts. The decryptor gets his secret key from a trust authority according to his attributes. However, he cannot decrypt any ciphertext or guess even what access structure was specified by the encryptor if his attributes do not satisfy the access structure associated with the ciphertext. All previous anonymous CP-ABE schemes are inefficient in that each ciphertext grows linearly with the number of attributes. In this paper, we propose an efficient anonymous CP-ABE scheme that reduces both the length of each ciphertext and the number of pairing operations to a constant level, but still leverages a hidden policy to keep recipients' privacy preserved. Furthermore, our scheme is fully secure in the standard model based on the decisional Bilinear Diffie-Hellman (DBDH) assumption in composite order groups. We remark that in our security definition, only the legitimate decryptor knows access structures associated with ciphertexts.