Based on Waters' attribute based encryption scheme, this paper proposes a two-party attribute based authenticated key exchange protocol with provable security in the standard model. The detailed proof of the security is presented in the modified BJM model under the decisional bilinear Diffie-Hellman assumption. In addition, to satisfy the requirement that the session key should not be escrowed by the trusted third party, a new protocol, which can cancel the escrow of the session key, is constructed from the basic protocol. The computation efficiency of the proposed protocols is nearly equivalent to the computation efficiency of the available ABAKE protocols with provable secure attribute in the random oracle model.