Extending the operating range of modern pump-turbines becomes increasingly important in the course of the integration of renewable energy sources in the existing power grid. However, at partial load condition in pumping mode, the occurrence of rotating stall is critical to the operational safety of the machine and on the grid stability. The understanding of the mechanisms behind this flow phenomenon yet remains vague and incomplete. Past numerical simulations using a RANS approach often led to inconclusive results concerning the physical background. For the first time, the rotating stall is investigated by performing a large scale LES calculation on the HYDRODYNA pump-turbine scale model featuring approximately 100 million elements. The computations were performed on the PRIMEHPC FX10 of the University of Tokyo using the overset Finite Element open source code FrontFlow/blue with the dynamic Smagorinsky turbulence model and the no-slip wall condition. The internal flow computed is the one when operating the pump-turbine at 76% of the best efficiency point in pumping mode, as previous experimental research showed the presence of four rotating cells. The rotating stall phenomenon is accurately reproduced for a reduced Reynolds number using the LES approach with acceptable computing resources. The results show an excellent agreement with available experimental data from the reduced scale model testing at the EPFL Laboratory for Hydraulic Machines. The number of stall cells as well as the propagation speed corroborates the experiment.