One of the main goals of E-UTRAN is to provide seamless access to voice and multimedia services with strict delay requirements, which is achieved by supporting handover from source cell to target cell. Proper handover algorithms can make the system increased capacity, better coverage, higher throughput, reduced latency requirements. In this paper we give an overview of the LTE intra-access handover procedure, the simulation approach, and several latest handover algorithms which can enhance performance of the LTE systems are introduced. Finally the results show that the handover in the LTE system is complicated and imperfect, proper handover algorithms in the LTE system should be researched as quickly as possible.