An accountable authority attribute-based encryption (A-ABE) scheme is presented in this paper. The notion of accountable authority identity-based encryption (A-IBE) was first introduced by Goyal at Crypto'07. It is a novel approach to mitigate the (inherent) key escrow problem in identity-based cryptosystems. In this work, the concept of accountable authority to attribute-based encryption (ABE) setting is generalized for the first time, and then a construction is given. The scheme non-trivially integrates an A-IBE scheme proposed by Libert et al. with an ABE scheme. In our construction, a user will be identified by a pair ( id, o~), where id denotes the user' s identity and ω denotes the set of attributes associated to the user. In addition, our construction is shown to be secure under some reasonable assumptions.