Greedy geographic routing is attractive in wireless sensor networks due to its efficiency and scalability. However, greedy geographic routing may incur long routing paths or even fail due to routing voids on random network topologies. We study greedy geographic routing in an important class of wireless sensor networks that provide sensing coverage over a geographic area (e.g., surveillance or object tracking systems). Our geometric analysis and simulation results demonstrate that existing greedy geographic routing algorithms can successfully find short routing paths based on local states in sensing-covered networks. In particular, we derive theoretical upper bounds on the network dilation of sensing-covered networks under greedy geographic routing algorithms. Furthermore, we propose a new greedy geographic routing algorithm called Bounded Voronoi Greedy Forwarding (BVGF) that allows sensing-covered networks to achieve an asymptotic network dilation lower than 4:62 as long as the communication range is at least twice the sensing range. Our results show that simple greedy geographic routing is an effective routing scheme in many sensing-covered networks.