In smart grid, a smart meter enables two-way communication between the meter and a central system for monitoring and billing purposes, so an authentication protocol is the fundamental of securing the operations of smart grid. In this article, we propose an authentication scheme based on S/Key one-time password scheme to provide mutual authentication between meters and the servers of smart grid. The proposed method can prevent impersonation attacks even if attackers break servers. Moreover, the proposed mechanism supports the verification function for examining service time-period.