The rotor side of a variable speed pumped storage unit adopts a special three-phase AC winding structure, and this makes it difficult to diagnose a short-circuit fault in the rotor winding. Therefore, this paper proposes an offline diagnosis method based on the principle of the repetitive surge oscillograph (RSO). First, the application scheme of the RSO method in the VSPSU is designed. Low-voltage pulses are injected into three phases of the rotor simultaneously and the response curve is detected to determine the fault condition of the unit. Then based on the analysis of the response characteristics of different short-circuit faults, an identification method for rotor winding short-circuit fault types and faulty phases is proposed. Subsequently, the variational mode decomposition-Teager energy operator (VMD-TEO) method is used to estimate the injected pulse and characteristic curve's initial sudden change position and then the fault position is determined by the time difference and the measured wave velocity. Finally, an exponential recovery fault factor is proposed to measure the severity of inter-turn short circuit faults to overcome the problem of amplitude overlap of characteristic waveforms caused by traveling wave attenuation. The simulation results show that the scheme proposed in this paper can accurately diagnose various rotor winding short circuit faults of a variable speed pumped storage unit.