VANETs (Vehicle Ad hoc NETworks) are highly mobile wireless ad hoc networks targeted to support vehicular safety and other commercial applications. Conventional routing protocols in MANETs (Mobile Ad hoc NETworks) are unable to fully address the unique characteristics in vehicular networks. On the other hand, some characteristics inVANETs, like mobility constraints and predicable mobility, can benefit routing in vehicular networks. It is known that vehicles tend to move more regularly. We propose a new position-based routing strategy with the consideration of nodes moving direction for VANETs, called DGR (Directional Greedy Routing). Considering the fact that vehicles often have predicable mobility, we propose PDGR (Predictive Directional Greedy Routing) to forward packet to the most suitable next hop based on both current and predicable future situations. We evaluate the performance of the solutions via simulations with realistic mobility models in open environments. Simulation results show that our solutions outperform existing ones in terms of packet delivery ratio, end-to-end delay, and routing overhead.