As a tradeoff of GEO and LEO, MEO satellite system has more acceptable service performance and it is more appropriate to provide global mobile communications. A MEO satellite system model communicating according to time slots is constructed in the paper. Moreover, in order to improve comprehensive performance of the network, a novel routing algorithm applying Time Evolving Graph based on Pairing Heap is proposed. The Time Evolving Graph is employed to analysis the dynamic topology of the network and the Pairing Heap is applied in the Dijkstra algorithm to reduce the time complexity. By contrast, Fibonacci Heap is also used to optimize Dijkstra algorithm. Finally simulation results show that routing algorithm applying Time Evolving Graph based on Pairing Heap can perform better and reduce the time complexity obviously, and at the same time, Pairing Heap works better than Fibonacci Heap when the number of nodes grows bigger.