Model checking is a very useful technique for verifying the network authentication protocols. In order to improve the efficiency of modeling and verification on the protocols with the model checking technology, this paper first proposes a universal formalization description method of the protocol. Combined with the model checker SPIN, the method can expediently verify the properties of the protocol. By some modeling simplified strategies, this paper can model several protocols efficiently, and reduce the states space of the model. Compared with the previous literature, this paper achieves higher degree of automation, and better efficiency of verification. Finally based on the method described in the paper, we model and verify the Privacy and Key Management (PKM) authentication protocol. The experimental results show that the method of model checking is effective, which is useful for the other authentication protocols.