3D unsteady turbulent simulations of runaway and load-rejection transients of the Francis turbine with RNG k- turbulence model are presented in this paper. Sliding mesh method is applied to the runner for both transients in order to obtain a time-accurate solution of the rotor-stator interaction, and dynamic mesh method is used to simulate guide vane closing for the load rejection transient. For the runaway transient, comparisons about unit discharge and unit speed are carried out between numerical predictions and experimental data when the Francis turbine arrives at the runaway situation, showing that the relative error of each parameter is in the range of ±5% and that the simulation method has good accuracy. As to the load-rejection transient, comparisons are made about rotational speed, pressure fluctuations at the spiral casing inlet and upstream of the tube cone between numerical predictions and measurement data, indicating that both rotational speed and pressure fluctuations at upstream of the tube cone are well predicted, yet there is some difference on pressure fluctuations at the spiral casing inlet. As a whole, the numerical method in this paper can predict both transients well, although some improvements should be made for further research.