A slewing-type working machine includes: a slewing motor which is a hydraulic motor for slewing; a variable-displacement hydraulic pump; a slewing operation device including an operation member; a control valve controlling the slewing motor based on an operation signal thereof; a pump regulator; a relief valve letting excess fluid to a tank; operation detectors detecting an operation direction and amount of the operation member; a motor rotational speed detector; and a controller controlling a discharge flow rate of the hydraulic pump. The controller obtains a deviation between a target rotational speed of the slewing motor obtained from a slewing operation amount and an actual rotational speed detected by the motor rotational speed detector, and controls the discharge flow rate to make the deviation closer to 0.