Smart Open Shortest Path First (S-OSPF), which is an extended scheme of OSPF, was previously presented to avoid network congestion. However, it is difficult to achieve S-OSPF implementation, since the S-OSPF architecture is different from the conventional OSPF network architecture. A conventional network requires an autonomous distributed routing architecture, but S-OSPF partly requires a centralized routing architecture while keeping the feature of the conventional network. We employ software-defined networking (SDN) technology to support S-OSPF. Edge routers in the S-OSPF network must have both traffic distribution function, which is a feature of S-OSPF, and OSPF-based forwarding function, which is used in case that the edge router behaves as a transit router as is in the original OSPF network. A conflict occurs on the common forwarding table, which is accessed by SDN and OSPF, in the edge router when we try to utilize existing software modules. To solve this issue, this paper proposes an implementation method by introducing a hybrid router with virtualization technique. A hybrid router by the proposed method achieves the traffic distributing function of S-OSPF as well as the OSPF behavior while minimizing the modification of existing routing software modules. We develop a prototype of the hybrid router, confirm that the traffic distributing function of S-OSPF and OSPF functions work correctly, and observe that the congestion is avoided in our experimental network.