Robust routing schemes are attracting attention as a routing scheme to achieve high robustness against changes in traffic patterns without performing both traffic measurement and dynamic change of traffic routes. This scheme, however, causes the performance degradation of TCP because it performs multipath routing and the out-of-order packet arrivals occur frequently. As a routing scheme to improve TCP performance while keeping high robustness against changes in traffic patterns, we proposed a robust routing scheme called MDD (Minimum Delay Difference). For every node-pair, the MDD selects the multiple routes with the minimum propagation delay difference between them as the candidate routes, and then derives the traffic distribution ratio of them so as to minimize the worst case link utilization ratio. According to the numerical example of the conventional research, however, TCP throughput of the MDD is about 70% of its ideal value and there is room for further improvement. In this paper, for the purpose of further improvement of TCP throughput, we propose a hybrid robust routing scheme. The scheme only selects a single candidate route for a predetermined ratio of node-pairs in order to avoid TCP performance degradation cause by packet reordering while it selects multiple candidate routes as well as the conventional scheme for the rest of node-pairs. Numerical examples show that, under the condition that the worst case link utilization ratio must be less than 1.0, our proposed scheme achieves at the maximum of 24% higher throughput than the MDD.