Attribute-based authenticated key agreement(ABAKA) protocol is used to establish session key among parties in the communication environment in which the identity information of individual is protected. Attribute-based extended Canetti-Krawczyk(ABeCK) model is a model with more security applying to the security proof of ABAKE protocol. This paper presents gap computational parallel bilinear Diffie-Hellman exponent(GCPBDHE) assumption based on gap computational Diffie-Hellman(GCDH) assumption. Based on Waters scheme, it establishes an ABAKA protocol, and proves its security in ABeCK model under GCPBDHE and CDH assumptions. Compared with the existing ABAKE protocols, the new protocol is more efficient in communication cost.