Escrowable identity-based authenticated key agreement (AKA) protocols are desirable under certain circumstances especially in certain closed groups applications. In this paper, we focus on two-party identitybased AKA schemes in the escrow mode, and present a strongly secure escrowable identity-based AKA protocol which captures all basic desirable security properties including perfect forward secrecy, ephemeral secrets reveal resistance and so on. The protocol is provably secure in the extended Canetti-Krawczyk model, and its security can be reduced to the standard computational bilinear Diffie-Hellman assumption in the random oracle model. Assuming no adversary can obtain the master private key for the escrow mode, our scheme is secure as long as each party has at least one uncompromised secret. Also, we present two strongly secure variants of the protocol, which are computationally more efficient than the original scheme.