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An Adaptive Probability based Reservation Strategy (APRS) was proposed for multimedia Low Earth Orbit (LEO) satellite networks. By making reservation based on mobile users' location information and handover probability, APRS controls the extent of priority placed on handover requests and reduces blocking probability for new connections. APRS also adjusts its reservation according to current network condition, and thus works well in the non-uniform traffic pattern. Simulation results show that the proposed strategy can reserve resources precisely and adaptively, trade-off the share of bandwidth between handover and new connections, and provide users with satisfactory Quality of Service (QoS) while maintaining bandwidth utilization high.