Due to the non-planarity of topological graphs for three-phase inverters, it is hard to construct three-phase current-source inverter (CSI) topologies from three-phase voltage-source inverter (VSI) topologies by using dual transformation. In order to form the multilevel CSI topology by making full use of the research findings of the three-phase multilevel VSI, two planar methods of treating with topological graphs of three-phase two-level voltage-source inverter topologies were discussed, and the feasibilities to construct three-phase multilevel CSI topologies by applying such methods were analyzed. By adding an extra voltage-source to the three-phase flying-capacitor multilevel VSI, an equivalent circuit topology with planarity was obtained, and a new kind of three-phase multilevel CSI topology was proposed through the dual transformation in this paper. Lastly, the multi-carrier sinusoidal pulse width modulation (SPWM) technique was adopted to verify the correctness and rationality of such multilevel CSI topology by simulation.