The goal of this paper is to look for relatively stable area in the Vehicular Ad hoc Network (VANET), thereby helping for developing more stable routing protocols. We built a theoretical model to analysis the stability of the VANET topology, and provided the simulation experiment to verify the correctness of the theoretical analysis. Results show that the vehicle traveling in the same direction is easier to maintain the stability of the topology of a VANET, and the valid time of the path will decrease with the increase of the intersection angle in the direction of the vehicle movement, the vehicle movement velocity and the time. In addition, the simulation results also show that the bigger the initial distance among the vehicles is, the less stable the network topology is. The discovery of this phenomenon is important to develop zoned routing protocols.