The Border Gateway Protocol (BGP) is an important inter-domain routing protocol, which is widely used in Internet. It allows independent policies to be designed for each Autonomous System (AS). However, the flexibility in designing independent policies causes the convergence problem, i.e., a BGP network may constantly send routing information between ASes and cannot reach a stable state. In this paper, we propose an approach for model checking the convergence property of BGP networks. We firstly establish a formal model of BGP networks and define its convergence property. Then we use the Promela language to describe this model and analyze its convergence. The model is generic enough, thus different instances of BGP networks can be simulated and verified by only modifying parameters and policies. Finally, as examples, we simulate and verify some typical instances of BGP networks by using the SPIN model checker.