Master key forward security is an important property for identity-based key exchange protocols. Unfortunately, most of existing identity-based key exchange protocols do not satisfy this property. In this paper, we firstly analyse Xie's modified protocol to show that signature is undesirable for an identity-based key agreement protocol with the master key forward secrecy. Then we present two improved protocols from McCullagh-Barreto identity-based key agreement protocol to capture the master key forward security. Our first protocol is efficient and its security can be proved with the help of a decisional oracle, while the second one achieves stronger security and its security can be reduced to a computational problem in the random oracle model. The master key forward secrecy is proved under the computational Diffie-Hellman assumption.