In a sudden load increasing process (SLIP), the hydroelectric generating system (HGS) experiences a severe vibration response due to the sudden change of the hydraulic-mechanical-electric parameters (HMEPs). The instability of HGS limits the ability of sudden load increase, and its flexibility and reliability are reduced. Thus, in this study, a new transient nonlinear coupling model of HGS is proposed, which couples the hydro-turbine governing system (HTGS) and the hydro-turbine generator shafting system (HGSS) with the hydraulic-mechanical-electric coupling force, rotating speed, flow rate, hydro-turbine torque, electromagnetic torque, and guide vane opening. By using numerical simulation, the influences of different HMEPs on the vibration characteristics of HGS in SLIP are analyzed. The result shows that, compared with stable operating conditions, the vibration amplitude of HGS increases sharply in SLIP. The increase of the sudden load increasing amount, blade exit flow angle, mass eccentricity and excitation current, and the decrease in guide bearing stiffness and average air gap between the stator and rotor cause abnormal vibration of different degrees in the HGS. Hydraulic factors have the greatest influence on the nonlinear dynamic behavior of HGS. The maximum vibration amplitude of HGS in SLIP is increased by 70.46%, compared with that under stable operating conditions. This study provides reasonable reference for the analysis of the nonlinear dynamic behavior of HGS in SLIP under the multiple vibration sources.