In the Tri-element Peer Authentication (TePA)-based wired Local Area Network (LAN) media access control Security (TLSec), the certificate-based wired LAN security association scheme has communication waste in the exchange key establishment processes and is not suitable for trusted computing environment. To solve these two problems, firstly, an improved certificate-based wired LAN security association scheme was proposed. In this scheme, the exchange key establishment process between the newly added switch and each nonadjacent switch was simplified, thus improving the communication performance of the exchange key establishment processes. Then, a certificate-based wired LAN security association scheme for trusted computing environment was proposed based on the above scheme. In this scheme, the platform authentication of the newly added terminal devices was added in the process of certificate-based authentication, so as to realize the trusted network access of the newly added terminal devices, and effectively prevent the newly added terminal devices from bringing worms, viruses and malicious softwares into the wired LAN. Finally, the two schemes were proved secure by using the Strand Space Model (SSM). In addition, through qualitative and quantitative comparative analysis, the two schemes are better than those proposed in related literatures.