A flow control apparatus and a flow control method for a construction machine are disclosed, which can perform ground leveling work for smoothing the ground by the self weight of a boom without supplying hydraulic fluid from a hydraulic pump to a hydraulic cylinder. The flow control method for a construction machine including a hydraulic pump, a hydraulic actuator connected to the hydraulic pump, a control valve controlling a flow direction of hydraulic fluid supplied to the hydraulic actuator, a work mode switching valve installed in a flow path between the control valve and the hydraulic actuator to perform switching between a normal work mode and a floating mode, a detection means for detecting a boom-down operation amount of an operation lever operated by a user, an electronic proportional valve controlling a discharge flow rate of the hydraulic pump, and a controller, the flow control method including a first step of determining whether the present mode is switched to the floating mode; a second step of changing the discharge flow rate of the hydraulic pump corresponding to the boom-down operation amount detected by the detection means if the present mode is switched to the floating mode; and a third step of outputting an electrical control signal to the electronic proportional valve so that the hydraulic pump can discharge the hydraulic fluid at the changed flow rate corresponding to the boom-down operation amount.