This invention is a hydraulic work machine having an electric assist motor coupled to an engine and a hydraulic pump, in the hydraulic work machine of which, a rotational speed and torque of the engine are controlled so that an operating point of the engine moves along a predetermined route for yielding a combustion state of the engine under a transient state that the engine changes in speed and torque. A target speed and torque of the engine 7 are set so that the rotational speed and torque of the engine 7 will change along a predetermined route F in a running region of the engine, respective rates of change of the target rotational speed and torque of the engine 7 are limited, and the engine 7 is controlled to yield the target engine speed. In addition, torque of the assist motor 10 is controlled to yield the target torque of the engine.