The main contribution of this work is to propose a novel call admission and handoff management scheme for LEO satellite networks. A key ingredient in our scheme is a companion predictive bandwidth allocation strategy that exploits the topology of the network and contributes to maintaining high bandwidth utilization. Our bandwidth allocation scheme is specifically tailored to meet the QoS needs of multimedia connections. The performance of our scheme is compared to that of various bandwidth allocation schemes proposed in the literature. Simulation results show that, compared with the other bandwidth allocation schemes, our scheme offers low call dropping probability (CDP), providing for reliable handoff of on-going calls and acceptable call blocking probability (CBP) for new calls.