The vast majority of routing approaches for vehicular ad hoc networks (VANETs) are distributed, which are ineffective to exploit the global networking information and easily lead to local optimum, appearing as sparse connectivity and network congestion. Recently, by combining software-defined network architecture together with VANETs, software-defined VANETs (SDVN) is widely concerned, which shows the benefits of centralized control. In this paper, we propose a hierarchical geography routing protocol for SDVN. First, the protocol divides a large region into multiple small grids according to the geographical location and finds a series of grids with good connectivity based on real-time grid vehicle density and historical vehicle transfer probability between grids. Second, we construct a path cost function with load balancing and keep two paths with minimal costs from the selected grids. Finally, a series of relay nodes on each selected path are filtered for routing according to node utility. Simulation results show that the proposed routing algorithm achieves significant gains in terms of delivery ratio, throughput, average delay, and average hop count compared with several existing routing protocols.