For hydraulic turbine, especially pump-turbine, the dynamic stress characteristics of runner during start-up is an important index to evaluate the stability of unit. Aiming to analyze the vibration response of a prototype Francis pump-turbine runner during start-up in turbine mode, focusing on the influence of the transient of the hydraulic excitation force on the dynamic stress. Firstly, the steady-state and local transient dynamic stresses were calculated for different rotating speeds during the start-up process. Then, the causes of abnormal vibration were discussed based on the modal analysis and the rotor-stator interaction analysis. Among them, the hydraulic excitation force was obtained by computational fluid dynamics analysis, and the dynamic stress was solved by acoustic-structure based one-way fluid-structure interaction method. Comparing the results of steady-state and transient analysis, it can be seen that the transient of the excitation force had a significant effect on the vibration response near the resonance working condition. The high-level vibration in the transition process laged behind the theoretical resonance condition, and the dynamic stress amplitude was far lower than that estimated by the steady-state method. But outside the resonance region, the dynamic stress levels obtained by steady-state calculation and transient calculation were very close. Besides, resonance was easy to occur only when a hydraulic excitation force corresponded to both the frequency and mode shape of a natural mode of the runner. The above results can provide a reference for the assessment of dynamic stress in the transition process.