A hydraulic pump controlling apparatus of a construction machine according to the present disclosure includes: a hydraulic pump in which a swash plate angle is controlled to control a discharge flow; an auxiliary pump; a control valve controlling a flowing direction of a fluid discharged from the hydraulic pump and selectively supplying the fluid to an actuator; an orifice and a relief valve connected between a center bypass line of the control valve and a tank T to be parallel to each other; signal pressure selecting units receiving a fluid passing through the center bypass line of the control valve and a fluid discharged from the auxiliary pump, and selecting the pressure of any one of the fluids as a signal pressure; and a regulator receiving the signal pressure selected from the signal pressure selecting units to control the swash plate angle of the hydraulic pump, and the signal pressure selecting unit selects the pressure of the fluid discharged from the auxiliary pump as the signal pressure and transfers the selected pressure to the regulator when the construction machine is in an idle state.