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In recent years, several IP-based algorithms have been developed for low-earth orbit (LEO) satellite networks. In this work, a new dynamic source routing algorithm in satellite constellation based on flood routing is developed. This source routing algorithm consists of such main mechanisms as route discovery, route maintenance, route cache and earth station agency, capable of processing routing tasks on-board and reducing the size of on-board memory by the cooperation of satellite nodes and earth station agencies. The performance of the DSRSC routing algorithm is evaluated through a simple Globalstar-like LEO satellite constellation network model. With the analysis and evaluation of performance, our new routing algorithm is suitable to be used in LEO satellite constellation network.