Smart-card is one of the most common cryptographic devices. Due to its tamper resistance characteristics, it has been widely used in many security-critical areas, such as e-commerce, medical health, and Internet of Things (IoT). However, with the development of side-channel attacks and reverse engineering, research shows that the parameters in the smart-card can be extracted, and the smart-card has no longer tamper resistance. Therefore, how to design multi-factor authentication protocols based on the non-tamper resistance smartcard has got a lot of attention. This paper studied two typical multi-factor authentication protocols in wireless sensor networks, pointing out that one cannot resist offline password guessing attacks and man-in-the-middle attacks, and fails to achieve mutual autentication, while the other cannot resist offline password-guessing attacks and fails to provide anonymity. In order to overcome these weaknesses, combined with the Hash-chain technique, a new non-tamper resistance smart-card based two-factor authentication scheme was proposed and formally proved secure under the random oracle model. Compared with other related multi-factor authentication schemes in the wireless sensor network environment, the proposed scheme could achieve higher security while maintaining lower computation cost. Consequently, it could be suitable for resource constrained wireless sensor network environment.