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Formal verification approaches can guarantee the correctness of security protocols. In this paper we take the well-known Needham-Schroeder public-key authentication protocol as an example, to show how we can apply the symbolic model checker for multiagent systems MCTK, which is developed by us, to the verification of security protocols. One temporal epistemic property is checked successfully both in the original version and the Lowe's revised version of the Needham-Schroeder protocol. The experimental result shows that our method is an effective way to the verification of security protocol.