Attribute-based signature (ABS, for simplicity) is an important cryptographic tool for anonymous authentication and access control.The signer uses his private keys to endorse the message on some predicate, and the verifier only knows that such a signature is from one of users satisfying the predicate if the signature is valid.In the traditional ABS, there is only one trusted central attribute authority who monitors and issues user attributes.In this paper, we first propose an efficient ABS with multiple authorities that can be proved with strong signer privacy and unforgeability in random oracle model.Signer privacy is enhanced due to the anonymous key-issuing protocol used in our scheme, that is, 1) the identity of signer is kept anonymous without revocation among all users satisfying the predicate given in the signature; 2) the user can get the attribute private key while preventing the authorities from linking attributes of the user.Furthermore,the unforgeability can be also achieved, where any user cannot forge a signature with a predicate if his attributes do not satisfy the predicate.