Recently, since many kinds of wireless devices have been widely used and a large amount of contents is available on the Internet, a network system that provides adequate services anytime and anywhere is required. In this research, we focus on satellite networks using mass storage devices to provide the above mentioned services. In this kind of network, multiple satellites are used to cover the whole surface of the earth, and each satellite is equipped with a mass storage device. By using mass storage devices, the satellite network can manage a high buffer capacity to handle large amounts of data. However, no routing method has been developed for such kind of satellite network that can utilize the storage devices and manage the large amount of data in the network effectively. In this paper, we propose a novel routing scheme for the efficient utilization of the mass storage on satellites to mitigate network congestion. The proposed method is analyzed mathematically. The numerical results validate the effectiveness of our proposed method.