A hydraulic working machine has an assist electric motor connected to an engine and a hydraulic pump. The emissions of air pollutants in the exhaust gas from the engine are minimized regardless of fluctuations in the load torque of the hydraulic pump. A specific revolution speed suitable for reducing the emissions of air pollutants is stored, and an engine is controlled using the specific revolution speed as a target revolution speed. The absorption torque of a hydraulic pump is subjected to high-pass filtering whereby a high-frequency component devoid of a trend component is obtained. Target assist torque is computed from the high-frequency component, and the assist electric motor is subjected to power running/generation control accordingly. A specific output torque range suitable for reducing the emissions of air pollutants is stored, and the target assist torque is corrected so that the trend component does not exceed the specific output torque range.