As the potential complement to terrestrial networks, satellite networks are expected to facilitate full coverage and broadband access at anytime and anywhere. However, satellite networks are characterized by highly dynamic topology and load, and how to design an adaptive routing algorithm to meet diverse application needs faces significant challenges. In this paper, we propose a Link-Attributes-based multi-service On-Demand Routing (LAODR) algorithm to provide highly reliable and service-aware data forwarding for Software -Defined Satellite Networks (SDSN). Specifically, we construct a quantitative model of link reliability which provides a fine-grained state description of the dynamic topology. Furthermore, we select the K-shortest path as the solution space and plan routing paths based on NSGA-II to allocate link resources reasonably. Extensive experiments on the Iridium validate that LAODR outperforms state-of-art routing algorithms in terms of end-to-end average latency, packet loss, throughput and node congestion degree, as well as meets the requirements of diverse services.