Since attribute–based signature (ABS) was introduced by Guo and Zeng in 2008, considerable researches have investigated this topic. In an ABS scheme, the attribute authority (A–authority) generates the private key for each user, hence, it has to be completely trusted. The A–authority is free to engage in malicious activities without any risk of being confronted in a court of law. Motivated by this, we firstly propose the notion of accountable attribute–based signature schemes in this paper. It is not only a variant of ABS, but also a new approach to mitigate the key escrow problem. Then, we construct two efficient accountable attribute–based signature schemes. Finally, we prove that the new schemes are secure under the computational Diffie–Hellman (CDH) and the modified computational Diffie–Hellman (MCDH) assumptions. Our main goal is to restrict the conditions that the A–authority can misbehave. In our schemes, if the A–authority maliciously generates and distributes a private key, it will run the risk of being caught and prosecuted.