Abstract: The certificateless-based authenticated key agreement protocols have the advantages of simplicity of managing identities compared to the PKI-based schemes，as well as avoiding the key escrow issues inherited in the identity-based schemes.This paper proposes a two-party certificateless-based authenticated key agreement scheme based on a provably secure certificateless-based public key encryption scheme.The comparisons with other comparable schemes in security and efficiency show that，the new scheme achieves more of the desired security attributes，such as perfect forward secrecy，PKG forward secrecy，known session-specific temporary information secrecy and key escrowless.Meanwhile it keeps the nice computational efficiency.