Satellite will continue play a major role in the implementation of the Next Generation Internet (NGI), with characters of large geographical coverage, unique broadcasting capabilities, and high-capacity channel. However, the dynamic network topology and limited on-board resources of satellite networks that involve non-geostationary satellites turn routing into a very challenging problem. In this paper, a distributed hierarchical routing protocol (DHRP) for non-geostationary satellite networks is developed which calculates routing tables efficiently using the collected link state advertisement. The protocol generates optimal paths with low implementation complexity and communicational overhead. The performance of DHRP is evaluated through analysis and simulations.