In this study, the authors propose a new efficient attribute-based signature (ABS) scheme. This scheme achieves existential unforgeability against selective predicate attack and attributes signer privacy in the standard model. The signature scheme only needs three pairing operations, and the signature size is constant, regardless of the number of attributes. Compared with other existing schemes, this construction provides better efficiency in terms of the computational cost and communication cost. To the best of author's knowledge, this is the first ABS scheme that can achieve constant signature size and constant number of pairing operations. In addition, after the analysis of Wang and Chen's attribute-based ring signature scheme, the authors show that their scheme is incorrect.