Currently, there is considerable emphasis on the electric pump-fed cycle for liquid engine, primarily due to its design simplicity. However, its development is hindered by the underdeveloped state of power battery technology. Drawing inspiration from hybrid power technology used in electric vehicles and turbochargers, a hybrid pump feed system for throttleable engines is originally proposed as a promising solution. This system integrates the electric motor into the gas generator cycle, with several topologies evaluated. The parallel configuration featuring a mid-motor is selected for its compact structure, efficient power-splitting and energy recovery. Additionally, customized energy management strategies and optimization models are developed to effectively allocate power throughout the operational processes of liquid engines. A comparative analysis of four engine cycles is conducted under the typically variable-thrust mission. The results indicate that attributed to the conservation of turbo-gas and battery energy, the optimized hybrid pump achieves a reduction of 2.39 % compared to the turbopump and 7.15% to the electric pump in total mass. Adaptability assessment further indicates that the mass advantage of the hybrid pump system is more significant during prolonged engine burning and deep throttling. Specific working conditions are found in which the system prefers electric-motor driving or regenerating turbine energy. Although energy-recovery results in the system efficiency decrease, it serves to lower energy demand of battery pack, thus easing the burden on cell thermal management and structural design. This study provides a practical design framework for hybrid pump-fed rocket engines in future variable-thrust missions.