Objective: Advanced equipment is the cornerstone of industrial modernization. New-energy vehicle manufacturing requires large servo presses to improve the quality and efficiency of automotive body stamping. However, the power fluctuation in such presses significantly increases grid capacity requirements. This study investigates the characteristics of power fluctuation in large servo presses with six-link mechanisms. Methods: Based on the principle of the six-link transmission mechanism, the kinematic model of the transmission system of the press was established, and the motion relationships between the bars, slider, and crank were obtained. Specifically, the expressions for the load torque, inertia torque, load power, and inertia power transmitted to the main motor shaft were derived, considering the stamping load and system inertia. Finally, an analytical model for the output power of the main motor was obtained. Taking the 2 500 t servo press produced by Jinan No. 2 Machine Tool Factory as an example, the fluctuation law of the output power of the main motor of the press during the stamping cycle and the cause of the peak power were analyzed by combining the analytical model and experimental data. Results: The established power analytical model can effectively capture the power fluctuation characteristics of a large servo press with a six-bar linkage. The main factors affecting the inertia power are the inertia and acceleration of the main transmission system of the press. Conversely, the main factors affecting the load power are the load applied to the slider and its speed. During the slider movement from the upper dead point to the starting point of the workpiece drawing, the inertia power initially increased and then decreased; the load power increased rapidly when the drawing pad started to operate. In the deep drawing stage of the workpiece, the inertia power fluctuated around zero, but the load power increased. During the upward movement of the slider from the bottom dead point, the inertia power initially decreased and then increased; the load power gradually decreased. The largest power peak was observed when the drawing pad started to operate, and the slider just crossed the bottom dead point; this is attributed to the speed fluctuations at both phases. When the drawing pad started to operate, speed fluctuation was caused by the rapid load increase, leading to a large positive power peak; when the slider just crossed the bottom dead point, speed fluctuation was caused by the change in the load direction, resulting in a large negative power peak. Conclusions: To reduce the impact of power fluctuations in servo presses on the grid side, it is necessary to reduce the load impact when the drawing pad starts to operate, and the slider just crosses the bottom dead point. When the hydraulic drawing pad starts to operate, the speed difference when it contacts the slider can be reduced by optimizing the motion control algorithm of the drawing pad. The load impact when the slider crosses the lower dead point can be suppressed by reducing the link clearance of the transmission system.