The research object was a Francis turbine, and the working conditions at 100%, 75%, 50%, 25%, and 1% opening were determined by the opening size of the guide vane. Large-Eddy Simulation (LES) was adopted as a turbulence model method to conduct three-dimensional unsteady turbulent numerical simulation of the entire flow channel of a Francis turbine, and the flow situation of various parts of the turbine under different working conditions was obtained. The flow characteristics of each component under different working conditions were analyzed, and the hydraulic performance of each part was evaluated. The factors that affected the stability of hydraulic turbines were identified, and their formation mechanisms and evolution laws were explored. The results show that the guide vane placement angle was reasonable in the guide vane area, and the hydraulic performance was fine. The impact on the stability of the hydraulic turbine was small. Further research showed that the hydraulic performance was poor in the runner area, and there were flow separation and detachment phenomena in the flow field. This created a channel vortex in the runner blade channel. The channel vortex promoted the lateral flow of water and had a significant impact on the stability of the hydraulic turbine. The diffusion section of the draft tube can dissipate most of the kinetic energy of the water flow in the draft tube area, and it had a good energy dissipation effect. However, the was a large pressure difference between the upper and lower regions of the diffusion section, and it generated a backflow phenomenon. It created vortex structures in the draft tube, and the stability of the hydraulic turbine was greatly affected.