Flux transfer events(FTEs) are local transient magnetic reconnections at the magnetopause(MP) that provide channels for transport of solar wind energy and plasma into the magnetosphere(MSP). All current theoretical models suggest that FTEs are open-flux ropes; however, global simulations show that they contain both open and closed magnetic fields. To clarify this topology, we analyzed 441 events observed by THEMIS and investigated their magnetic topologies. Only one type of open field line was detected in most magnetosheath(MSH) FTEs, independent of the polarity of the Bn bipolar signatures. Newly formed MSH field lines were also observed. In the all MP boundary layers FTEs and most MSP FTEs, multiple types of topologies were observed, irrelevant to the Bn bipolar polarity. Closed field lines were found in all MP boundary layers and MSP FTEs. Meanwhile very few boundary FTEs contained the newly formed MSH flux. In some situations, only closed field lines were seen in MSP FTEs, which are referred to as the fossil FTEs. These results, which largely differ from the traditional view, demonstrate the existence of complex magnetic topologies in FTEs. Based on these results, we propose a new 3D FTE picture to modify the current FTE models. Flux transfer events (FTEs) are local transient magnetic reconnections at the magnetopause (MP) that provide channels for transport of solar wind energy and plasma into the magnetosphere (MSP). All current theoretical models suggest that FTEs are open-flux ropes; however, global simulations show that they contain both open and closed magnetic fields. Only one type of open field line was detected in most magnetosheath (MSH) FTEs, independent of the polarity of the Bn bipolar signatures. Newly formed MSH field lines were also observed. In the all MP boundary layers FTEs and most MSP FTEs, multiple types of topologies were observed, irrelevant to the Bn bipolar polarity. MP boundary layers and MSP FTEs. When very few FTEs contained in the newly formed MSH flux. In some situations, only closed field lines were seen in MSP FTEs, which ar These results, which largely differ from the traditional view, demonstrate the existence of complex magnetic topologies in FTEs. Based on these results, we propose a new 3D FTE picture to modify the current FTE models.