The electro-hydraulic power source with an electro-hydraulic variable pump driven by a servo motor is suitable for electrified construction machinery. To achieve better energy efficiency in different working conditions, the multi-mode control scheme was proposed for the electro-hydraulic power source. The control scheme includes pressure control, flow control, and torque control modes. The switching rule among the three control modes was formulated based on the minimum pump pressure. The fuzzy PID controller was designed, and a composite flow regulation strategy was formulated, including the load-sensitive adaptive displacement regulation and servo motor variable speed regulation. The AMESim-Simulink co-simulation model of multi-mode control was established. The test platform was built, and the experimental study was carried out. The results indicate that the fuzzy PID control has a shorter response time and a more stable control effect compared with PID control. Additionally, the composite flow regulation strategy improves the flow regulation range by 36% and reduces the flow overshoot by 20% compared with the load-sensitive adaptive displacement regulation. As the main control valve received an opening step signal, the full flow regulation (7~81 L/min) of the power source took approximately 0.5 s to rise and 0.2 s to fall. The relative error of pressure difference for the main control valve was 0.63%. When receiving the pressure and torque step signal, the pump pressure and pump input torque both took approximately 0.45 s to rise and 0.2 s to fall. The relative errors of pump pressure and torque control were 0.2% and 0.16%, respectively. In the multi-mode control, the electro-hydraulic power source could switch smoothly between flow control mode, pressure control mode, and torque control mode. These results provide a reference for the multi-mode control of an electro-hydraulic power source with an electro-hydraulic variable pump driven by a servo motor.