Trusted network access protocols are proposed for the security and authorization of network-access requests. Because they differ greatly from traditional security protocols on security demands, they can not be analyzed with previous strand space works directly. To solve this problem, we first give some extensions necessary to verify them in this letter. Moreover, we point out Zhuo Ma et al.'s MN-TAP protocol is unsecure based on the Strand Space Model (SSM), and then improve the MN-TAP protocol and show that the improved MN-TAP protocol is secure in the SSM.