The pumped-storage power stations (PSPSs) with variable speed units (VSUs) have been emerging in recent years, and the research on the transient processes of those PSPSs is of great significance. In this paper, the transient processes of a PSPS with four units, i.e. three fixed speed units (FSUs) and one VSU, sharing one tunnel are numerically simulated under the conditions of large fluctuation and small fluctuation. Firstly, combining the calculation method of hydraulic transient processes and the basic equations of pump turbine, doubly-fed induction motor (DFIM) and governor, a hydraulic-mechanical-electrical coupling model of PSPS is established. Secondly, the data of an actual PSPS is substituted into the model and the corresponding parameters are set. Then, the transient processes of typical conditions of large fluctuation and small fluctuation are simulated respectively. Finally, according to the numerical simulation results, the characteristics of the transient processes of PSPS with three FSUs and one VSU are analyzed. The results show that, under large fluctuation conditions, whether the initial operating states of FSUs and VSU are consistent or not, the transient processes are similar. Under small fluctuation conditions, the VSU can adjust the active power to meet the grid demand more quickly than the FSUs.