A hydraulic swing-controlling apparatus of a work machine comprising: a hydraulic pump installed in the work machine; a swing motor which receives supply of hydraulic oil from the hydraulic pump and swings the work machine; a swing relief valve (3a, 3b) which defines the upper limit of a pressure of the hydraulic oil in an oil-hydraulic circuit connecting between the hydraulic pump and the swing motor during operation of the swing motor; a hydraulic pressure detecting means which detects a hydraulic pressure supplied from the hydraulic pump to the swing motor; a swing operation amount detecting means which detects the amount of the swing operation related to a swing motion of the swing motor; a required flow rate setting means which sets a required flow rate (F R) of the hydraulic oil required for the swing motor based on the amount of the swing operation detected by the swing operation amount detecting means; and a relief flow rate estimating means which estimates a relief flow rate (F E) of the hydraulic oil relieved from the swing relief valve (3a, 3b) based on the hydraulic pressure detected by the hydraulic pressure detecting means, wherein the relief flow rate estimating means includes an estimated relief flow rate setter; and a minimum relief flow rate setting means which sets the minimum relief flow rate (F MIN) desired to be relieved from the swing relief valve (3a, 3b); and a subtracter which calculates the relief flow rate (F E) by subtracting the ensured minimum relief flow rate (F MIN) set by the minimum relief flow rate setter from an estimated relief flow rate set by the estimated relief flow rate setter; wherein a pump flow rate subtracting means calculates an appropriate flow rate (F D) by subtracting the estimated relief flow rate set by the estimated relief flow rate setter from the required flow rate (F R) set by the required flow rate setting means and by adding the minimum relief flow rate (F MIN) set by the minimum relief flow rate setting means; and wherein a discharge flow rate controlling means controls the discharge flow rate of the hydraulic pump based on the appropriate flow rate (F D) calculated by the pump flow rate subtracting means; wherein the estimated relief flow rate setter sets the estimated relief flow rate based on the hydraulic pressure and the override characteristics of the swing relief valve (3a, 3b). a hydraulic pump installed in the work machine; a swing motor which receives supply of hydraulic oil from the hydraulic pump and swings the work machine; a swing relief valve (3a, 3b) which defines the upper limit of a pressure of the hydraulic oil in an oil-hydraulic circuit connecting between the hydraulic pump and the swing motor during operation of the swing motor; a hydraulic pressure detecting means which detects a hydraulic pressure supplied from the hydraulic pump to the swing motor; a swing operation amount detecting means which detects the amount of the swing operation related to a swing motion of the swing motor; a required flow rate setting means which sets a required flow rate (F R) of the hydraulic oil required for the swing motor based on the amount of the swing operation detected by the swing operation amount detecting means; and a relief flow rate estimating means which estimates a relief flow rate (F E) of the hydraulic oil relieved from the swing relief valve (3a, 3b) based on the hydraulic pressure detected by the hydraulic pressure detecting means, wherein the relief flow rate estimating means includes an estimated relief flow rate setter; and a minimum relief flow rate setting means which sets the minimum relief flow rate (F MIN) desired to be relieved from the swing relief valve (3a, 3b); and a subtracter which calculates the relief flow rate (F E) by subtracting the ensured minimum relief flow rate (F MIN) set by the minimum relief flow rate setter from an estimated relief flow rate set by the estimated relief flow rate setter; wherein a pump flow rate subtracting means calculates an appropriate flow rate (F D) by subtracting the estimated relief flow rate set by the estimated relief flow rate setter from the required flow rate (F R) set by the required flow rate setting means and by adding the minimum relief flow rate (F MIN) set by the minimum relief flow rate setting means; and wherein a discharge flow rate controlling means controls the discharge flow rate of the hydraulic pump based on the appropriate flow rate (F D) calculated by the pump flow rate subtracting means; wherein the estimated relief flow rate setter sets the estimated relief flow rate based on the hydraulic pressure and the override characteristics of the swing relief valve (3a, 3b).