The investigation of the rotating stall phenomenon appearing in the HYDRODYNA pump-turbine reduced scale model is carried out by performing a large-scale large eddy simulation (LES) computation using a mesh featuring approximately 85 × 10^{6} elements. The internal flow is computed for the pump-turbine operated at 76% of the best efficiency point (BEP) in pumping mode, for which previous experimental research evidenced four rotating stall cells. To achieve an adequate resolution near the wall, the Reynolds number is decreased by a factor of 25 than that of the experiment, by assuming that the flow of our interest is not strongly affected by the Reynolds number. The computations are performed on the supercomputer PRIMEHPC FX10 of the University of Tokyo using the overset finite-element open source code FrontFlow/blue with the dynamic Smagorinsky turbulence model. It is shown that the rotating stall phenomenon is accurately simulated using the LES approach. The results show an excellent agreement with available experimental data from the reduced scale model tested at the EPFL Laboratory for hydraulic machines. The number of stall cells as well as the propagation speed agree well with the experiment. Detailed investigations on the computed flow fields have clarified the propagation mechanism of the stall cells.