The potential of infrastructureless vehicular ad hoc networks (VANETs) for providing multihop applications is quite significant. Although the Epidemic Routing protocol performs well in highly mobile and frequently disconnected VANETs with low vehicle densities or light packet traffic loads, its performance degrades greatly in environments of high vehicle density together with heavy packet traffic loads that create serious bandwidth contention and frequent collisions. We propose a new epidemic routing protocol in urban environments called Greedy Zone Epidemic Routing (GZER), in which the neighbors of a vehicle are divided into different zones according to their physical locations. Each vehicle maintains a summary vector (SV) of packets buffered locally and zone summary vectors (ZSVs) of all packets buffered in each zone. Whether the infection will be transmitted in each zone is decided by the difference between SV and ZSV. Simulation results show that the proposed GZER protocol outperforms the existing solutions significantly, especially in the environments of high vehicle densities together with heavy packet traffic loads.