This paper focuses on the issues of admission control and rerouting for LEO satellite networks providing multimedia services. The issues includes resource allocation and routing for intersatellite links (ISLs), load balance amongst links. and satellite handover and rerouting caused by satellites ' dynamic characteristics. Applying Markov Decision Process (MDP) theory and generic policy-iteration formulation. a distributed routing scheme, called adaptive cost routing (ACR), is proposed. Comparing the performance of ACR with other routing schemes in terms of system throughput and blocking rate, the ACR presented itself with not only a better routing performance, but also less connection setup time and easier to be implemented in contrast to most centralized routing algorithms.