We propose a new concept called 'flow rule virtualization' (FlowVirt) for programmable network virtualization (P-NV). In P-NV, network hypervisor is a key component in that it plays a role in creating and managing virtual networks. This paper first reports a critical limitation of network hypervisor - scalability problem, which results in the high consumption of the switch memory, control channel, and CPU cycles: 3.9, 4.7, and 1.7 times higher than host-based network virtualization, respectively. This scalability problem arises because all the flow rules from the virtual network controllers are directly installed into switches. To resolve the scalability problem, FlowVirt introduces a flow rule abstraction: virtual and physical flow rules. By separating virtual and physical flow rules, the abstraction virtualizes flow rules so that FlowVirt can merge virtual flow rules to a smaller number of physical flow rules to be installed in switches. The evaluation results show the enhanced scalability of FlowVirt. The number of flow rules to be installed in switches decreases by up to 10 times compared to the previous P-NV. The control channel bandwidth and CPU cycles are also reduced by up to 14 and 3 times, respectively.