This paper proposes a simple shortest-path-based load-balanced Internet-Protocol (IP) routing scheme based on the hose model. The proposed scheme is an extension of the Smart-OSPF (S-OSPF) scheme. The proposed scheme, the same as S-OSPF, splits traffic demand only at source edge nodes and transmits the traffic along the shortest path routes. In S-OSPF, the split ratios are determined for each source-destination edge node pair by assuming that the traffic demand between all source-destination edge node pairs are known, in other words, the exact traffic matrix is completely given. This, however, is difficult to measure and predict accurately because of the measurement costs and rapid traffic fluctuations. On the other hand, in the proposed scheme, we assume the use of the hose model; in this model, only the total amount of traffic that a node injects into the network and the total amount of traffic it receives from the network are known. This simplicity makes it easy for network operators to apply the hose model for IP routing. This is because measuring just the total amount of traffic is less expensive than measuring the traffic demands between all source-destination edge node pairs. In addition, the aggregated traffic exhibits less fluctuation and is easier to predict than the traffic demand between each source-destination pair. Any extension of the Linear Programming (LP) formulation that optimizes S-OSPF to suit the hose model cannot be solved as a simple LP problem, because the traffic matrix is not known. By introducing a duality theorem, we successfully formulate our problem as an LP formulation that can be easily solved yielding the desired split ratios. Numerical results show that the proposed scheme dramatically reduces the network congestion ratio compared to the classical shortest path routing scheme and it provides performance close to that provided by the sophisticated traffic-engineering (TE) scheme of Multi-Protocol Label Switching (MPLS)-TE.