Non-Geostationary Earth Orbit (NGEO) satellite networks such as Low Earth Orbit (LEO) satellite networks and Medium Earth Orbit (MEO) satellite networks are suitable solutions to provide global communication services with low power consumption and short delay. Additionally, Multi-Layered Satellite Networks (MLSN) which consists of layered NGEO satellite networks has recently attracted attention due to their increased capacity and number of available multipath. However, in MLSN, one should take into account the features of each layered network, i.e., lower layer networks provide a short delay connection with high risk of occurrence of network congestion, and vice versa. While several existing schemes have been developed to efficiently use layered networks, these methods can cause network congestion by biased traffic distribution to one of the network layers. To cope with this issue, we propose a route control method which attempts to distribute appropriate amount of traffic to each network layer. In our proposed method, a threshold is defined according to end-to-end delay of traffic. Long distance traffic which tends to cause network congestion by passing through many links is forced to be sent through MEO layer. By deciding the threshold properly, we can avoid deep network congestion, and in consequence, capacious network services are provided. To assess the validity of the proposed scheme, we ran computer simulations by using a two-layered MLSN constructed by combining a LEO and a MEO satellite networks. The results showed improved performance of the proposed scheme especially in terms of packet drop rate and total throughput in the network.