Concerning the problem of invulnerability in Vehicular Ad Hoc NETwork (VANET), the invulnerability characteristics for VANET under random attacks and intentional attacks were analyzed. Firstly, the largest connected component, average size of components, critical point removal ratio as well as network efficiency were proposed to be used for the invulnerability evaluation metrics for VANET. Then, based on intelligent driver model with lane changes, the VANET was established through VanetMobisim software. Finally, the influence of the number of nodes, transmission ranges and patterns of attack on VANET invulnerability were given. The experimental results show that the VANET has a strong invulnerability faced with random attacks while its invulnerability to intentional attacks is fairly low as a result of the uneven degree distribution of vehicles; the intentional attacks based on node betweenness destroy the networks more quickly and strongly. The derived rules can provide the optimization of VANET topology control, protocol development and network management with new guidance.