The invention discloses a topological structure of a high-power density power electronic transformer and a control method for the topological structure. A group of series resonance circuits (or band-pass filters formed by other components) are added to a bridge arm branch with N cascaded H bridge submodules at a high voltage AC side, and meanwhile, a high-frequency signal is superposed into a modulating wave signal to transmit energy of the high voltage AC side to a low voltage side in a high frequency manner. According to the topological structure, one series resonance circuit is directly formed through cascaded H bridges, an LrCr series resonance circuit and a high-frequency isolation transformer at the high voltage side to output a high-frequency waveform and to achieve energy transmission. A large number of DC-DC conversion modules are saved, meanwhile, power switching devices applied to the high voltage AC side are also greatly reduced, the volume and the cost of a system are greatly reduced, the work efficiency of the system is improved and the power density of the power electronic transformer is improved.