Cognitive wireless networks are vulnerable to message tampering, forgery, eavesdropping, and denial of service attacks due to the openness of wireless channels and the broadcasting characteristics of wireless transmission. In order to resist these attacks, researchers have proposed many physical layer authentication technologies. Compared with traditional cryptographic authentication mechanism, physical layer authentication technology is faster and more efficient, so it is very suitable for continuous and real-time authentication of resource-constrained terminals in cognitive wireless networks. However, the existing physical layer authentication technology can not achieve the initial authentication, and packet loss events often occur in the authentication process, resulting in long authentication delay and low authentication efficiency. This study combines traditional cryptographic authentication technology with physical layer authentication technology, and proposes a lightweight cross-layer authentication scheme. The scheme only uses cryptography technology in the initial authentication, while the other authentication uses fast and efficient physical layer authentication technology, which improves the authentication efficiency. In this scheme, an improved normalized statistic is used, which makes the calculation of threshold simpler, reduces the computational complexity effectively and reduces the user authentication waiting delay. In addition, the Hash chain-based authentication method is adopted to ensure that continuous authentication can still be achieved in case of packet loss. Performance analysis shows that, compared with existing schemes, the scheme in this study has greater advantages in improving authentication efficiency.