With the development of Wireless Sensor Network (WSN), user authentication in WSN is a critical security issue due to their unattended and hostile deployment in the field. To improve the security of user authentication, a new provably-secure two-factor authentication key exchange scheme based on Nam's first security model was proposed. The proposed scheme was based on elliptic curve cryptography, and it achieved authentication security and user anonymity. The safety of the improved protocol was proved based on ECCDH in the random oracle model. Performance analysis demonstrates that compared to Nam's schemes, the proposal is more efficient, and it is more suited to wireless sensor networks environments.