Vehicular ad hoc network (VANET) standards, including IEEE 1609 WAVE and ETSI C-ITS, use IPv6 to interconnect VANET with the Internet. Considering the high vehicle speeds and short communication ranges of road side units (RSUs), such vehicles may suffer from frequent service interruptions. Several VANET IP mobility schemes have been proposed in order to mitigate this problem. However, these only support L3 handover, as the RSUs act as IPv6 access routers (ARs) for vehicles. Some VANET IP mobility schemes reduce the handover latency of the L3 handover but do not fundamentally mitigate the frequency of the L3 handover. As L3 handover indicates that the default router of the vehicle is changing, the vehicle must perform IPv6 configuration, including router discovery and neighbor unreachability detection. Since most L3 handover latency is caused by this IPv6 configuration, the L3 handover involves a higher signaling cost and longer handover latency than the L2 handover. We propose a network-based L2 extension handover scheme for VANET. It decouples the AR functions from the RSU. An AR connects several RSUs via L2 links within its coverage. In this configuration, most inter-AR handovers are replaced with intra-AR handovers, so that the frequency of the L3 handover is decreased substantially. Therefore, the service disruption time caused by default router switching is also reduced, and the deployment of VANET can be made more flexible by decoupling the RSU and the AR. Proxy Mobile IPv6 is adopted in order to support inter-AR handover in the proposed scheme. Furthermore, the scheme supports seamlessness in both the intra-AR and inter-AR handovers with buffering at the AR. The performance analysis and the simulation result reveal that the proposed scheme reduces the signaling cost and handover latency and also shows seamless packet delivery for vehicles.