Ensuring a seamless connection when users are moving across radio cells is essential to guarantee a high communication quality. In this paper, performance of TCP during the handover in a Long Term Evolution (LTE) network is investigated. Specifically, mobile users with high bit rates TCP services are considered, and the impacts of the intra LTE handover over their perceived throughput are studied. Due to the mobility of the users across radio cells, the high bandwidth required, and possible network congestions, it is shown that the handover may cause sudden degradation of the quality of the communication if the process is not correctly controlled. To alleviate these problems, three solutions are proposed: fast path switch, handover prediction, and active queue management. The first two solutions avoids excessive delay in the packet delivery during the handover, whereas the second solution acts at the transport network with an active queue management. Simulation results, obtained by an extension of the ns-2 simulator, show that the proposed solutions present advantages, and that the handover prediction used with the active queue management increases TCP performance significantly.