In Vehicular Ad Hoc Networks (VANETs), directional antenna is a good solution if a longer transmission distance is needed. When vehicles are equipped with directional antennas, however, complete paths from the sources to the destinations there may not exist. Epidemic routing protocol is considered as one of the well-performed routing protocols when the networks are intermittently connected but it can cause a heavy load to the network and great energy consumption to the nodes. First in this paper, we propose a novel neighbor discovery algorithm which makes nodes be able to sense the topology changes around them and arrange their directional antennas accordingly. Secondly, we propose a routing protocol which is based on the conventional epidemic routing protocol, and nodes make their routing decisions according to the information collected during the neighbor discovery process. Experimental results show that the proposed neighbor discovery algorithm has better performance especially in the scenario where the node density is low. Moreover, the matching routing protocol can effectively reduce the load of the network and successfully deliver the packets to its destination in a reasonable short delay.