In hydraulic work machines having an electric assist motor 10 linked to an engine 7 and a hydraulic pump 6, there is provided a hybrid-driven hydraulic work machine capable of maintaining the torque of the engine at a prescribed value when the load on the hydraulic pump 6 is higher than the rated power of the engine 7 and the electric assist motor 10 assists the torque of the engine. The hybrid-driven hydraulic work machine comprises: target engine revolution speed calculation means 11a which sets a target revolution speed of the engine at a particular revolution speed; engine control means 21a which controls the engine revolution speed based on the target revolution speed of the engine; engine load calculation means 11b which calculates an engine load; and at least one selected from the following: electric motor power running calculation means 11c which calculates a differential revolution speed between the target engine revolution speed and the revolution speed of the engine and performs power running control on the electric assist motor depending on the differential revolution speed when the engine load is a prescribed value or higher; and hydraulic pump absorption torque calculation means 11d which performs reduction control on absorption torque of the hydraulic pump depending on the differential revolution speed when the engine load is a prescribed value or higher.