Key negotiation can establish a shared key between two or even multiple parties in a public networkenvironment, ensuring communication confidentiality and integrity. Certificateless public key cryptography(CL-PKC) aims to achieve succinct public key management without using certificates, while avoiding thekey escrow property in identity-based cryptography. As an important part of CL-PKC, certificateless authentication key agreement (CLAKA) has also received widespread attention. Most CLAKA protocols are constructed from bilinear mappings on elliptic curves which need costly operations. To improve theperformance, some pairing-free CLAKA protocols have been proposed. In this paper, we propose a multifactor authentication CLAKA protocol that can achieve local authentication factors joint unlocking. Theprotocol does not require bilinear pairing computation and has been proven to be secure under the mBRmodel.