This study proposed a novel handover bicasting scheme for long term evolution (LTE) system. The conventional bicasting scheme makes the bicasting decision according to signal-to-noise ratios (SNR) to minimize the packet delay time and aim at seamless connectivity during the handover processing period. However, the SNR-based bicasting scheme cannot optimize the efficiency of backhaul resource utilization and quality of service (QoS) for users. Instead of using SNR as the traditional bicasting mechanism does, the proposed bicasting scheme exploits packet success rates (PSR) as the link quality estimator during the handover processing time in order to simultaneously reduce the waste of backhaul resources and provide QoS for users. Neural networks (NNs) are used to learn the correlation function between PSR and relative metric indicators, e.g. SNR, packet length, bit error rate (HER), and so on, and then to generalize the learned function for the whole cases of interest. We conducted simulations to compare the performance of our proposed scheme with that of SNR-based scheme. The results illustrate that our approach can effectively reduce the waste of system resources and improve user-perceived QoS in comparison with the SNR-based scheme, and thus enhance the overall efficiency of L TE networks.