In this paper, we propose a new algorithm that improves the performance of the operation of Handover (HO) in LTE-Advanced (LTE-A) networks. As recognized, Mobility Management (MM) is an important pillar in LTE/LTE-A systems to provide high quality of service to users on the move. The handover algorithms define the method and the steps to follow to ensure a reliable transfer of the UEs from one cell to another without interruption or degradation of the services offered by the network. In this paper, the authors proposed a new handover algorithm for LTE/LTE-A networks based on the measurement and calculation of two important parameters, namely the available bandwidth and the Received Power (RSRP) at the level of eNodeBs. The proposed scheme named LTE Available Bandwidth and RSRP Based Handover Algorithm (LABRBHA) was tested in comparison with well-known algorithms in the literature as the LHHA, LHHAARC and the INTEGRATOR scheme using the open source simulator LTE-Sim. Finally, the network performances were investigated via three indicators: the number of lost packets during the handover operation, the latency as well as the maximum system throughput. The results reported that our algorithm shows remarkable improvements over other transfer schemes.