A method for controlling a hydraulic pump system for a construction machine including a variable displacement hydraulic pump, a hydraulic actuator connected to the hydraulic pump, a control valve controlling hydraulic fluid supplied to the hydraulic actuator when shifted by signal pressure that is in proportion to an operation rate of an operation lever, a first detection sensor detecting the operation rate of the operation lever, and a control unit controlling a discharge flow rate of the hydraulic pump in accordance with a detection signal from the first detection sensor, the method comprising: a first step of detecting the operation rate of the operation lever by the first detection sensor; a second step of calculating a flow rate that is required in the hydraulic pump in accordance with the operation rate of the operation lever; a third step of comparing and determining levels of the calculated flow rate and a preset dead-zone value; a fourth step of calculating a flow increasing rate as the calculated required flow rate if the calculated flow rate exceeds the dead-zone value; a fifth step of comparing and determining levels of the calculated flow increasing rate and a preset flow increasing rate limit value; a sixth step of setting the discharge flow rate of the hydraulic pump to the flow increasing rate limit value that is lower than the flow rate required in the hydraulic pump in accordance with the operation rate if the calculated flow increasing rate exceeds the flow increasing rate limit value; and a seventh step of setting the discharge flow rate of the hydraulic pump to the required flow rate in accordance with the operation rate if the calculated flow rate is lower than the dead-zone value in the third step, wherein in the case of accelerating a swing movement of an upper swing structure that is driven by the hydraulic actuator, the flow rate supplied to the hydraulic actuator is reduced by limiting the discharge flow increasing rate of the hydraulic pump with lapse of time characterized in that the hydraulic pump system further comprises a second detection sensor installed in a discharge flow path of the variable displacement hydraulic pump to detect discharge pressure of the hydraulic pump, wherein a torque is calculated using the detected pressure and a volume of the hydraulic pump, and the volume of the hydraulic pump is reduced so that the increasing rate of the calculated torque value is limited with the lapse of time. a first step of detecting the operation rate of the operation lever by the first detection sensor; a second step of calculating a flow rate that is required in the hydraulic pump in accordance with the operation rate of the operation lever; a third step of comparing and determining levels of the calculated flow rate and a preset dead-zone value; a fourth step of calculating a flow increasing rate as the calculated required flow rate if the calculated flow rate exceeds the dead-zone value; a fifth step of comparing and determining levels of the calculated flow increasing rate and a preset flow increasing rate limit value; a sixth step of setting the discharge flow rate of the hydraulic pump to the flow increasing rate limit value that is lower than the flow rate required in the hydraulic pump in accordance with the operation rate if the calculated flow increasing rate exceeds the flow increasing rate limit value; and a seventh step of setting the discharge flow rate of the hydraulic pump to the required flow rate in accordance with the operation rate if the calculated flow rate is lower than the dead-zone value in the third step, wherein in the case of accelerating a swing movement of an upper swing structure that is driven by the hydraulic actuator, the flow rate supplied to the hydraulic actuator is reduced by limiting the discharge flow increasing rate of the hydraulic pump with lapse of time characterized in that the hydraulic pump system further comprises a second detection sensor installed in a discharge flow path of the variable displacement hydraulic pump to detect discharge pressure of the hydraulic pump, wherein a torque is calculated using the detected pressure and a volume of the hydraulic pump, and the volume of the hydraulic pump is reduced so that the increasing rate of the calculated torque value is limited with the lapse of time.