Based on the characteristics of guaranteed handover (GH) algorithm, the finite capacity in one system makes the blocking probability (PB) of GH algorithm increase rapidly in the case of high traffic load. So, when large amounts of multimedia services are transmitted via a single low earth orbit (LEO) satellite system, the PB of it is much higher. In order to solve the problem, a novel handover scheme defined by multi-tier optimal layer selection is proposed. The scheme sufficiently takes into account the characteristics of double-tier satellite network, which is constituted by LEO satellites combined with medium earth orbit (MEO) satellites, and the multimedia transmitted by such network, so it can augment this systematic capacity and effectively reduces the traffic load in the LEO which performs GH algorithm. The detailed processes are also presented. The simulation and numerical results show that the approach integrated with GH algorithm achieves a significant improvement in the PB and practicability, as compared to the single LEO layer network.