Wireless sensor networks (WSNs), which consist of a large number of sensor nodes, have become among the most important technologies in numerous fields, such as environmental monitoring, military surveillance, control systems in nuclear reactors, vehicle safety systems, and medical monitoring. The most serious drawback for the widespread application of WSNs is the lack of security. Given the resource limitation of WSNs, traditional security schemes are unsuitable. Approaches toward withstanding related attacks with small overhead have thus recently been studied by many researchers. Numerous studies have focused on the authentication scheme for WSNs, but most of these works cannot achieve the security performance and overhead perfectly. Nam et al. proposed a two-factor authentication scheme with lightweight sensor computation for WSNs. In this paper, we review this scheme, emphasize its drawbacks, and propose a temporal credential-based mutual authentication with a multiple-password scheme for WSNs. Our scheme uses multiple passwords to achieve three-factor security performance and generate a session key between user and sensor nodes. The security analysis phase shows that our scheme can withstand related attacks, including a lost password threat, and the comparison phase shows that our scheme involves a relatively small overhead. In the comparison of the overhead phase, the result indicates that more than 95% of the overhead is composed of communication and not computation overhead. Therefore, the result motivates us to pay further attention to communication overhead than computation overhead in future research.