An apparatus and method for controlling a control valve, and a method for controlling a discharge flow rate of a hydraulic pump for a construction machine are disclosed, which can control a spool shifting speed of a directional valve and a discharge flow rate of a hydraulic pump in accordance with a hydraulic fluid temperature in winter season with below zero temperatures. The apparatus for controlling a control valve includes a variable displacement hydraulic pump; a hydraulic actuator driven by hydraulic fluid that is supplied from the hydraulic pump; a control valve installed in a flow path between the hydraulic pump and the hydraulic actuator and shifted to control a start, stop, and direction change of the hydraulic actuator; an operation lever outputting an operation signal corresponding to an operation amount; a temperature sensor detecting a hydraulic fluid temperature of a hydraulic fluid tank connected to the hydraulic pump; and a controller applying a control signal that corresponds to the operation amount of the operation lever 3 to the control valve if the hydraulic fluid temperature detected through a signal from the temperature sensor is higher than a predetermined temperature, and adjusting the operation signal according to the operation amount of the operation lever in a predetermined increment rate to correspond to the detected hydraulic fluid temperature and applying the adjusted control signal to the control valve if the hydraulic fluid temperature detected through the signal from the temperature sensor is lower than the predetermined temperature.