The Internet of Things technology allows devices automatically connect with others or a server for the purposes of exchanging data. People can conveniently integrate data from those devices for a smart home, vehicular ad-hoc network, e-Health, etc. In 2017, Wang et al. proposed a simple authentication scheme for the Internet of Things. Although they formally proved that their scheme is secure, they did not consider the privacy of devices and stolen verifier attack. In this paper, we first demonstrate the weaknesses of Wang et al.’s scheme. Accordingly, we present a higher security level authentication scheme to resist the above weaknesses.